There are 5 such achievements and you will get them just by going through the game since they are story-related. No point to discuss them here. Beat the game and they are yours.

Actually you may find them all just by a sheer chance, but at least first two are really easy to miss. If you did then just return back to a previously finished level.

Achieved on the level 3-2. The name is self-explanatory. Some things could be right under your nose, but you may never see them if you don't look at them right.

If you really can't see the solution even after a few hours then here is an explanation how to do this. Please, don't read this if you still believe in yourself.
Seriously? OK, you asked for this. After pressing that orange button at the top rotate the top part to reveal a ladder at a side, climb it to the top and rotate the scene until part of the staircase in the middle will appear right under your feets. Stand on it and rotate scene clockwise once. Move to top of the ladder. Rotate scene clockwise once more. Proceed to the exit.

Achieved on the level 11-2. Move and move and do what the ghosts usually do. The wizards do this to reach some fractional platforms.

If you really can't figure out how to "break the game" even after my tip then read the spoiler.
Okay, it's your choice. Rotate the top part, go through the door, rotate the top part and climb it to the middle. Rotate the top part counterclockwise. Click at the platform next to the closed door and rotate the top part clockwise right after that click. If you do it right your robot will go through a wall and disappear in it. Well, actually through a floor or ceiling if you haven't rotated the bottom part.

If you GOTTA GO FAST or analphabetic or both then most likely you will get this on your own. I think you can do this at any level. Achieved on level 1.

Well, I can't say anything here since I haven't figured this one without a spoiler myself even though it's the easiest among the 3. You have to spam clicks during the cutscenes to skip them as soon as possible.