Fill each of the piece of the puzzle with one of the 4 available colours. Don't let pieces of the same colour touch (share a side).
Try and use as few colours as possible when solving a level. Many of them can be completed in 3 or less. (Check the level select menu to see which ones you have left.)
I convinced the artist responsible for the music to join the NG community. Credit has been given accordingly! (Go check his stuff out and tell him to make more :P)
Sorry about the lack of "achievements". If I could give you guys some "medals" for winning I totally would. (Hint some admin should totally give me access to the AS3 Medals API :P)