Try shooting your grappling hook at it.

What's the best way to move a box from afar?

that if you have the gun set to red and stand as far to the right as possible, you can move the big blue block above you by jumping and shooting at its lower left corner.

There's only so many distinct objects in this room. Examine them all.

Go right. Pick up Grapple Gun.
Shoot sticky part of ceiling with Grapple Gun.
Jump on button. Go right.
Shoot switch with Grapple Gun.
Move on.

Go right. Shoot switch with Grapple Gun.
Go further right. Shoot sticky ceiling with Grapple Gun.
Stand on the edge of the platform.
Shoot sticky floor with Grapple Gun.
Shoot switch with Grapple Gun, turning it off.
Jump up and shoot sticky wall with Grapple Gun. Land on button.
Fall down. Shoot switch with Grapple Gun.
Go all the way to the right.
Shoot sticky ceiling with Grapple Gun.
Continue.

Move right. Shoot gear with Grapple Gun.
Pick up sticky box.
Go to the right and up.
Set sticky box on the rightmost green door.
Press leftmost yellow button.
Stand on rightmost yellow button.
Shoot sticky box with Grapple Gun.
Pick up box and finish level.

Move right. Jump up, using door as a platform.
Go right. Pick up box.
Set box on rightmost yellow button.
Pick up other box.
Set box on leftmost yellow button.
Go back and pick up the first box.
Set the first box on top of the second box.
Jump up the boxes and go left to get the Squit Cannon.
Use the Squit Cannon to get back up.
Use the Squit Cannon to get up to the exit!

Use the Squit Cannon to get to the button.
Press the button.
Go back down and get the lantern.
Set the lantern down at the bottom of the shaft leading up to the candle.
Make a web platform.
Quickly pick up the lantern and jump up to the next blue platform.
Repeat twice. Light lantern with candle.
Use lantern to burn gas clouds.
Use the Squit Cannon to get to the exit.

Use the Squit Cannon to reach the green button and press it.
This will bring the lantern to the other side of the door.
Pick up the lantern, stand on the yellow button, and set it down.
Put some sticky webs right above the elevator, so that the lantern stops on top of it.
Pick up the lantern and throw it onto the ice and let it slide to the elevator.
Remember to keep standing on the yellow button.
Use web platforms to get to the other side of the level.
Push the yellow elevator button.
The lantern will burn the gas clouds and allow you to reach the exit.

Hold D and constantly jump until you get to the laser marker.
Use it to find a pathway through the room.
(Sorry, you'll actually have to put some effort into this one).
Remember to start by triggering the switch to open the door!

Use the laser to find out what symbol is obscured by the smoke cloud.
Trigger the switch with this symbol above it.
Go back and mark the smoke cloud again (the symbol will have changed).
Trigger the switch with this symbol above it.
Mark the smoke cloud one last time. Note also that the symbols change every time you play the level.
Trigger the switch with that symbol above it.
If at any point you trigger the wrong switch, you have to start over.
After getting three switches right in a row, you can go on to the next room.

The button on the left moves the boxes backwards, the button on the right moves them forward.
The blue laser switches turn the circles clockwise and counterclockwise.
Use the boxes to jam the circles in place and line them all up.
Then pull the boxes out, rotate the circles so the holes are facing you, and shoot the switch.
At that point, the door will open and you can proceed.

Go right.
Pick up box, jump on elevator.
Throw box onto yellow button while standing on elevator.
Jump up and pick up lantern. Light lantern on candle.
Use lantern to melt ice blocks, get Spike Bow.
Use lantern to light arrows on fire, then shoot them through the tunnel to melt the last ice block.
Walk through the door and proceed.

Use Spike Bow to hit switch. Time it carefully.
Go right. Shoot an arrow up to hit the switch.
Remember to run right as soon as you fire the shot, otherwise the door will close on you.
Fire a shot to hit the lower switch.
Stand close to where the closed door used to be, and hit the other switch again.
Remember to run through before the door closes.
Get the box, place it between the doors.
Hit the switch again, remembering to run through the door before it closes again.
Use the box to hold down the yellow button.
Shoot an arrow up so that it is lit by the torch and melts the ice block.
Keep going.

Go down and pick up Grapple Gun.
Light an arrow on fire with the lower torch.
Use it to light the upper torch.
Use the Grapple Gun to get back up.
Hit the switch with the Spike Bow. Time it carefully.
Light an arrow on fire, and use it to melt the ice block.
Also trigger the switch on the floor.
Quickly light an arrow on fire and shoot a moving lantern with it.
Quickly switch to Grapple Gun and use it to get to the closed door.
Quickly shoot the switch and move right before the door closes.
Fully charge a shot and aim straight across.
Shoot the lantern as it falls. If you time it right, the ice block will be melted.
Shoot the gear with the Grapple Gun. If you fall, quickly move left and land on the door so you don't die.
Proceed.

Pick up Polarity Beam.
Use beam to push box aside.
Use box to get up.
Use small box to push button and open door.
Push large box aside to reach polarity changer.
Change the polarity, pull the small box back off the button.
Continue.

Pick up small orange box and place it on yellow button.
Stand on the right edge of bottommost large red box.
Aim the polarity beam at the box's top left corner to ride it over to the left.
Suck the large blue box on top of it.
Push the red box (the blue box will move with it) until they're close to the edge.
Put the blue box slightly to the right side of the red box, so that they can be used as steps.
Step up and change the polarity.
Go right and suck down the newly presented large red box.
Ride it across the spike pit. Do not change the polarity.
Push the large blue box into the hole and press onward.

Push the small blue box onto the button.
Change the polarity and go right. Push the large red box until it won't go any further.
Pick up Squit Cannon.
Change the polarity back to blue.
Use web platforms to get up the shaft the red box was blocking.
Go down the shaft to the left and suck the box back so that the right shaft is unblocked.
Go back up and down the right shaft.
Set lantern on the red platform. Change polarity to red.
Go back up the shaft, then down the left shaft and push the box to the right side.
Go down the center shaft.
Change the polarity.
Push the red platform until it's past the yellow button.
Stand on the yellow button and push it the rest of the way.
Suck the blue button all the way to the left to knock it down and burn the gas cloud.
Cross the gap. Suck the blue platform all the way to the right.
Use web platforms and the blue platform to get to the level's end.

Use the moving platform to cross the gap.
Use the conveyor belt to do a long jump across the next gap.
Pick up box.
Stand on elevator and throw box onto yellow button.
Pick up Grapple Gun.
Go back down, take box off yellow button.
Stand on elevator and throw box onto button again.
Right before the elevator stops moving, shoot the switch and jump up.
You can proceed at this point.

Shoot all three switches.
Put one box in each claw.
Jump across the boxes, shooting the switches on the way.
The boxes will fall down and open the doors.
Pick up Polarity Beam.
Shoot all three switches again, place all three boxes again.
Make sure the blue box is on the leftmost claw.
Use the same method you used before to get across.
Use the Polarity Beam to push the blue box off the switch, making sure you're past the door when it closes.
Go onward.

Put both boxes on the yellow buttons. The blue box should be on the rightmost one.
Use the yellow pushing thingy to get up.
Shoot the switch. This will make the conveyor belt turn the other way.
Push the blue box off of its button.
Suck the red platform over to you, then suck it back to the left.
Push the blue box to the right so you can grab onto the sticky box.
Use the Grapple Gun to get up there and trigger the switch.
Get on the right side of the conveyor belt.
Use the momentum from the conveyor belt to hurl yourself over to the switch.
Shoot the switch.
Now go back over until you come to the rightmost red moving platform.
Carefully stand on the right edge of this small platform, and suck yourself over to the right.
Change the polarity.
Drop down.
Push the leftmost red platform all the way to the right.
Put the blue crate on the left button this time, and the red crate on the right button.
Use the yellow thing to get up there again.
Push the red box off the button.
Shoot the switch to make the conveyor belt turn clockwise again.
Push yourself to the left and grapple the box again.
Use the conveyor belt to hurl yourself over to the top right, suck the box out of the way, and proceed.

Pick up Laser Marker.
Activate the echo switch.
Go right.
Put the box directly under the shaft leading to the new echo switch.
Shoot an echo bubble up, open the door for it by shooting the laser switch, and detonate it when it comes near the echo switch.
Continue.

Use the bottom left laser switch to bring the elevator down.
Stand on the elevator and use the top switch to carry yourself up.
Jump onto the left platform and pick up the block stack.
Set it on the yellow thing. It will snap into place.
Hold down the yellow button to push up the laser box.
Take the laser box.
Toss the laser box down.
Take the block stack and toss it down as well.
Set down the block stack right below the lower left laser switch.
Set the laser box on top of it.
This will hold open the door and allow you to trigger the echo switch.
Continue.

Go up to the top left.
Drop through the blue platform and set the laser box on the conveyor belt.
Set the laser angle changer on the yellow button, then use the top left laser switch to bring down the laser box.
Leave them there for now.
Get under the echo switch and trigger it, opening the door to the box.
Use the laser box and the laser angle changer as a platform to get up to the box. Toss the box down.
Set the box on the conveyor belt at the top right.
Set the laser box to the left of the rightmost laser switch.
Set the laser angle changer directly below the middle laser switch. It will snap into place.
Stand next to the closed door just before the exit, and shoot a laser into the angle changer.
Watch the magic happen.
Proceed.

Go up and pick up the bomb.
Use the candle to light it on fire, then get it next to the brick wall.
The brick wall will be destroyed. Continue to the second bomb.
Use the second bomb as a step to get up to the Spike Bow.
Set the bomb next to the brick wall.
Shoot an arrow so that it hits the candle then falls down on the bomb.
Go onward.

Pick up the first bomb, stand on the left elevator, and throw it onto the yellow button.
Light an arrow on fire with the candle, then use it to light the bomb.
Jump off the elevator before the bomb explodes.
When the bomb explodes and opens the door, get the Squit Cannon.
Use the Squit Cannon to get to the far side of the level.
Light an arrow on fire with the candle at the bottom right, then use it to light the rightmost bomb.
Go back to the other side of the level.
Set a bomb on the left elevator, then stand on the elevator yourself and use another bomb to press the switch.
Now we have to be just a little fast. Toss the bomb on the elevator onto the ledge, light an arrow on fire, light the bottom bomb, set another arrow on fire, jump up, light the top bomb, pick it up, and run through the door to explode the brick wall. Don't worry, bombs can't hurt you.
Press the green button to congratulate yourself. And also let you access the other elevator.
Get a bomb (again), shoot the switch next to the rightmost elevator to bring it down, put the bomb on it, then send it back up and use the Squit Cannon to follow it.
Put the bomb next to the brick wall blocking the exit.
Drop down, use the candle to light an arrow on fire, and light the bomb with that arrow. If you're finding it hard, put the bomb closer to the edge.

First we need to get rid of the gas cloud.
Take the leftmost bomb, shove it onto the conveyor belt, and when it comes down (lit), use it to light an arrow, then shoot that arrow into the gas cloud.
The torch should light. If not, just repeat the process for the torch.
Use that torch to light the other torches.
Now go back up to the bomb. Make a web platform that's almost halfway up the jump to the next platform, but not quite.
Pick up the bomb, jump on that web platform, and jump up higher. Set the bomb on the top of this platform.
Use more web platforms to get up yourself.
Set this bomb on the elevator.
Using the torch to light an arrow, set the bomb on fire and quickly press the yellow button to send it up to the switch, which it will trigger.
Now the door to another bomb is open. Yay.
Use this bomb to destroy the brick walls at the bottom. (This can be done earlier, but you don't actually need to do it until now)
Go and pick up a bomb (either one) and then use the yellow things to get yourself up to the top - bomb in hand, of course.
You'll come to a place that's too low for you to pass under. As it happens, however, you can throw a bomb through it, so do that.
Repeat process for the other bomb.
Now use the Squit Cannon to get up from the other side. Put one bomb next to the brick wall, and the other one on the left edge of the conveyor belt.
Use a flaming arrow, lit by the nearby torch, to light the bomb. Then quickly press the yellow button.
The first bomb will trigger the second bomb, destroying the barrier and permitting you to pass.

Shoot the switches to make the laser machines mark the platforms and sticky spots. From there it's just a walk to the exit.

Get the Laser Marker. Use it on the semitransparent blocks to make platforms.
This allows you to cross the first part.
Continue using the Laser Marker to map out the room.
Once you come to a red block, a door, and an echo switch, use a laser to erase the red block and an echo marker to trigger the switch.
Grapple the ceiling and continue. You'll come to more yellow blocks.
They'll stop the laser from going through, so use echo markers to find grappleable areas. Make some platforms to land on after grappling them, and you just need to get to the exit at that point.

Here's a little twist.
Start by studying the layout. Then use the green button to turn off the lights.
Use the laser switches to rotate the circle with holes. Then use the three switches (in any order) to fire the lasers and hit the laser switches. You'll have to adjust the position of the circle after every switch.
If you make a mistake, it resets.
If you succeed, the door opens.
Do the same for the next, only this time you have two circles to contend with.
Use the crosses to tell you when you have the right rotation.
After opening both doors, you're finally done, and can continue to the next level.

Place the laser box on the button. Jump up to get the sticky box.
Put the laser box on the yellow thing now, and the sticky box on the button.
You can now obtain the Grapple Gun, so do that.
Use the Grapple Gun to shoot the switch.
Now move the sticky box off the button and put the laser box on the button.
Take the sticky box up and set it on the little mound.
Take the laser box off the yellow button and set it so that it triggers the bottom laser switch.
Use the Grapple Gun to get to the sticky box, grab it, and place it on the conveyor belt.
Now put the laser box back on the button, climb up, and grapple yourself across.
Now just go up to the exit.

Stand on the button until the wheel is wound all the way up, then quickly jump up and grapple it.
Alternative: Just jump up. Slightly harder but still easy.
Get the Squit Cannon.
Use it to get to the other side of the level. (Use the right mouse button to make grappleable webs since the gas clouds destroy platforms).
Push the green button. Toss the box across to the other side.
Go back to the other side, put some webs on the ice near the gap to stop the box there.
Go down to the bottom, put a web on the box (which should be plugging the gap) and grapple yourself up. Go onward.

Go all the way to the right and get the bomb. Shove it through the gap in the platform to your immediate left.
Get to the other side of that platform with the Squit Cannon.
Use the bomb as a platform to get up to the switch and trigger it.
Take the bomb with you to the other side and put it on the yellow button.
Here comes the hard part. Put a web on the block that comes down, quickly take the bomb off the switch and throw it away, put a web on the leftmost top corner, then use the Grapple Gun to get yourself up, right, up.
Press the green button to burn the gas clouds.
Go over to the right and get the second bomb. Put it on the moving block.
Put the other bomb back on the yellow button. The brick walls at the bottom will be destroyed.
Go up and toss the bomb down there again, only follow it down this time. Quickly shove it down so it blows up the other bomb, then jump up and go through the door.
You'll fall on the green switch and open the door to victory. Congrats.

Get the Grapple Gun and continue to the right.
Go up and shoot the force bomb to detonate it.
Now that the blue block has been cleared away, simply grapple the ceiling, press the green button, go back down, and proceed.

Take the force bomb, set it in the middle of the floor, shoot it, and stand on top.
Jump up right before it detonates to launch yourself up.
Set the next force bomb right below the switch, shoot it, and shoot the switch. Right before it explodes, start running to the right. The force of the explosion will push you under the closing door in time.
Go to the right as far as possible. Put the force bomb as far right as possible and use it to catapult yourself up, then drop down so you can get the Laser Marker.
Grapple yourself back up. Put the force bomb on the leftmost yellow button, and move the ice cube to the left door.
Use the Laser Marker on the semitransparent block to make a platform, then set the force bomb on it. Quickly get to the rightmost yellow button and press it. Right before the platform disappears, shoot the bomb with the grapple gun.
Wait.
The force bomb will push the ice block all the way to the right.
Now just run to the exit. Yup.

Get to the green button in the middle of the level. Easily done.
Press it to obtain a box.
Put the box in front of the tunnel to the yellow button, then use a force bomb to shove it in. It may take two.
Now line up the three force bombs behind it.
Shoot the one in the back. It will cause the other two to push the box to the yellow button.
If it doesn't do it the first time (and it probably won't) just line up the bombs again. It'll push the box a little further in every time.
Your reward? Another force bomb...as if three isn't enough. Well, actually, three isn't enough.
Put one force bomb in each of the three holes in the center of the level, and one above the wooden slats at the left.
Now it's time for a race. Go to the bottom, put the bottom right force bomb in the middle of the floor, shoot it, and shoot the upper one through the wooden slats. Use the force bomb nearest to you (that you shot first) to catapult yourself up. The race is on.
Get to the yellow button at the far right as quickly as possible. If you do it before the last force bomb explodes, you've beaten the timer and will be given the ice block to use as a platform to the exit. If the bomb explodes before you hit the button, you were too slow and you need to set the whole thing up again.
Do you really need a guide to tell you to use the ice block as a platform to get up the exit? You're pathetic. Anyway, use the ice block as a platform to get to the exit.

Stomp on the icy green button and then continue to the ice block.
Toss it to the left so it hits the icy red button, and right before it lands on the button, jump up.
This should let you get up to the top.
Now get the second ice block, stand against the yellow button, and toss it to the left while running after it. Jump on top of it and jump off again to get over the first hurdle to the green button, then use it as a stool once again to get to the button.
Press the button. Self-explanatory.
Proceed.

First go to the left and press the green button. Pick up the ice block that appears, toss it to the left, and hit the icy green button right before it comes to the last red block.
It will press the green button and allow you to get the Spike Bow.
Press the icy red button and then go up. Shoot the switch to turn the green blocks on.
Jump on the leftmost block, shoot at it again, but jump to the right before the green blocks disappear. If done correctly, you'll get to the next platform.
Stand next to the red blocks blocking your way and shoot the switch one last time.
Position the box on the very left edge of the top green block.
Position the laser box on the left edge of the regular box.
Jump up the shaft until you come to a closed door, then shoot the switch. Repeat until at the top.

Shoot the first color switch to pass the red blocks.
Shoot the second one to pass the green blocks.
Shoot the third one and stand on the green block.
Shoot it again.
Shoot it once more, but jump up and to the left before the arrow hits it.
Standing atop the red blocks, shoot the switch again.
Go as far left as you can, and shoot the switch protected by wooden slats.
Immediately before the arrow hits, jump up and to the right to stand on a ledge.
Then jump to the left to enter the tunnel.
Proceed to the left, up, right, down. You'll come to a box, a switch, and some other crud.
Use the box to block the red outline, then go back and shoot the color switch again.
Stand on the yellow button and shoot the green switch.
Now use the box as a stepstool to proceed to the top of the level.
Stand on the rightmost red block, and shoot the color switch twice. As soon as you fire the second arrow, jump up to the right.
Stand on the very edge of the rightmost red outlines, then fire two arrows at the bottom color switch.
Proceed.
ALTERNATE: If you cleverly use the green blocks near the bottom as a step to get up to the red platforms, you can skip most of the level.

Pick up Grapple Gun.
Shoot the sticky ceiling at the left, then the sticky box. Pick up the box.
Use the yellow thing to get upstairs.
Stand on the edge of the icy platform and toss the box to the left. Fall down to the right and shoot the box as it falls.
This will put you on the green button, which will open the door to the next room, so continue.

Pick up Polarity Beam.
Push the big blue box out of the corner and all the way to the right. Then suck the red sticky box down.
Change the polarity and push it down the hole.
Change the polarity again and suck it as far to the left as it will go.
Change the polarity once again, push the sticky box the rest of the way to the left, grapple the box, and suck yourself up on the elevator.
Go to the right until you come to the Squit Cannon. Switch it out, leaving the Grapple Gun on the ground, not the Polarity Beam.
Press the green button.
Go down to the wooden slats and find a blue box, an ice block, and an elevator.
Put some sticky webs on the ice block to stop the blue box there.
Give the blue box a gentle suck.
Now the blue box should be on top of the ice block. Go up to the top (you can use web platforms or grapple the ceiling), stand on the yellow button, and change the polarity when the door opens.
Push the big blue box into the hole and continue.

Use the Grapple Gun and Laser Marker.
Shoot the force bomb and turn the semitransparent block into a platform. The newly created force bomb will land on it.
Shoot that force bomb, keeping the platform bright.
When the force bomb gets close to detonating, switch guns and go to the left a little.
Right before the bomb detonates, shoot the sticky box.
The sticky box will be pushed to the left and you will be pulled with it, onto the button.

Use the Spike Bow and Grapple Gun.
Get the color switch to light up green only. Then shoot it and jump up right before the arrow hits.
Now shoot it again, to light up both colors.
Go up and a little to the left. Shoot the next switch until it lights up only green, then stand in the center of the red outline and shoot it again until it lights up only red. Jump up, stand on the wooden slats, and shoot it again until it lights up only green.
Stand on the green blocks further to the left, and shoot it twice. Naturally you must jump up and to the left right before the second arrow hits.
Now just press the button.

This requires the use of several guns. Start with the Squit Cannon and Laser Marker.
Use the semitransparent platforms and web platforms to get the lantern up to the ledge on the left.
Now that the lantern is up there, go back and switch the Laser Marker for the Polarity Beam.
Use web platforms to stay under the elevator, and push it up with the Polarity Beam.
Once it's all the way up, switch out the Polarity Beam for the Spike Bow.
Get up to the yellow button, hold it down, and shoot an arrow through the torch and onto the lantern on the elevator.
Now go back, switch the Spike Bow for the Polarity Beam, change the polarity to red, and suck the lit lantern down.
Switch the Polarity Beam back for the Spike Bow again, and shoot through the elevator lantern onto the other lantern. You may have to reposition the unlit lantern.
Now take the newly lit lantern and burn the gas cloud. Use web platforms to get up to the button and press it.
Continue to the end of the game. Yes, the statistics are random, except for Accuracy.