There will be spoilers, especially the game map.

There are 3 palettes initially available, and 10 more to be collected. They do not contribute to any completion metric, but it's tracked in your save file.

Compared to chips, palettes often contain puzzles that require extremely obscure mechanics or very out-of-the-box thinking.
Most if not all palette puzzles can be solved without dying (compared to chips where you need to survive to have the chip count); doing otherwise would often trivialize the challenge.

In this guide, palettes are order by their room's X coordinate. I denote the coordinates by X,Y where X is horizontal right and Y is vertical up, with the starting room as 0,0.



p.s. If you're stuck on the last two chips, you need to take look at the teleport mechanics.

(The game map is too big for Steam guide so I'm hosting it on imgur)

https://i.imgur.com/gZJFnpx.png

Legend
White: Start
Yellow: Ability
Green: Warp
Red: Chip
Cyan: Palette

Location: At the top-right of the starting screen

How to get it: Hold left/right when starting from this screen to land on the letters, then jump up.

This is only possible after the initial opening sequence, or after an ending sequence, since they're the only time you're spawned above this screen.

Location: Before Warp 2, at the screen where you first learn jumping to disable blocks enabled by electricity

How to get it:
You can only get it when you get your ability (which means not until you come back later).

Throw your head to the right of the next screen and stand between the screen boundary. Then jump up; the blocks will support you after your head lands to the floor. Keep jumping up, then jump right and grab the palette, and get your head before you explode.

Location: After warp 3, the 2nd set of two stack of barrels, drop down at the center

How to get it:
Checkpoints will not activate if the head is not attached to the body.

After opening the door, throw the head through the checkpoint in the corridor, then proceed as normal.

Location: After warp 3, the 3rd set of two stack of barrels, drop down at the center

How to get it:
When there is no input for a while, the robot will fall asleep and stop producing electricity.

Stand on the moving platform, then wait until the idle state kicks in, so the platform will send you to the other side. Then jump out of the platform.

Location: After warp 5, on the left on the screen holding the 3 pistons that come down to let you jump up

How to get it:
Electric conductivity of the map is affected by hidden walls.

Throw the head at the entrance to keep the hidden wall disabled. Get the door key, then go back and pick up your head. Proceed.

Location: After warp 5, there is a suspiciously half-empty screen with a lone platform sticking on top of the corridor. Touch the wall on the right for a while until a platform comes down.

How to get it:
You can reset platform states multiple times.

Move the platform to the right. Throw your head upwards the gap, then reset the state so the platform catches your head.
Then reset it again soon so the head is at the left side of the platform.
Then drop the head when it reaches the ground on the left.

Location: After warp 5, after the spot where you need to reach around a piston then reset it to drop down to below. There is a hidden wall to the left.

How to get it: There is no puzzle here. Just throw your head somewhere, get the palette then get your head back. Make sure your head isn't stuck inside the 1-height corridor.

Location: After warp 5, just after the screen where you have to survive a moving platform against a 7-height line of fire traps and fall down, there is another hidden wall to the left.

How to get it:
You need to perform a pixel perfect jump.

Once you manage to jump on the 3-height blocks without disabling them, getting the door key is easy.

Location: After warp 6, on the right of the screen where a piston comes down EXTREMELY quickly

How to get it:
You need to perform a precise jump at the right time.

Throw your head upward, drop down, then perform a precise, well-timed jump up to catch your head between the platforms. If done correctly, the head will go past the platform, allowing you to use it below and reach the palette.

Location: After warp 6, at a platform ladder, where the ladder keeps going up

How to get it:
The door itself is conductive.

Throw your head on the door as you stand on the electric blocks. Jump up and get the door key, which will open the door and hence disrupt the connection, allowing you to escape. Proceed.