Really cool game. The art is awesome to look at. The code needs some work, but that's more than understandable given the one week time limit.
However, here's a few easy tips:
There seems to be a cling mechanic, but I suspect that it was implemented because the character was sticking to walls anyway. To remedy that, create a "Physics Material 2D" in your project window, and set the friction to 0, then apply that to your character or walls; this will make it so he slides down the walls instead of sticking.
The character doesn't move with platforms, and there's probably a million different ways to fix this, but the way I know how to do it is to make the player a child of the platform whenever he's touching it; that will allow him to move with it (un-child him when he leaves the platform).
I don't want to sound too negative, I did manage to beat the game, and it's one of the coolest games I've played thus far. Nice work.