I don't get it. I can't figure out how to beat the level.
I love this game so incredibly much, that I went through the 3-4 puzzles again just for you (and even if they're not the right puzzles, I still enjoy playing the game anyway).
There are two puzzles in this level, both involving green-sparkly switches. Stuff that sparkles green means that they are not affected by your time travel.
The first puzzle, as soon as you open the door, a goomba-guy falls to his death. activate the green switch and reverse time back to the beginning. The goomba will land on the platform, going into the hole and getting the key for you. Jump on him to get the key, and flip the platform the other way to get the puzzle piece on the other side behind the locked door.
The second puzzle is a bit trickier. It is a puzzle piece next to a spike pit, covered by a sparkly-green platform. The trick to this one is using your time-travel to go through the platform, then drop down onto the puzzle piece.
Flip the lever so you can cross, then climb up the ladder and stand above the puzzle piece for a couple seconds. Climb back down the ladder, flip the switch again, then time-travel your way back to where you were standing above the puzzle piece. You can then grab it, and time-travel back to the lever to complete the level.