Level skip
At the game selection screen in story mode, press L1, Square, R1(2), R2, Square, L1, R1, R2.

Big heads
While playing the game, press Up, Left, Down, Left, Down, Up(2), Left.

Low gravity
While playing the game, press Up(6), Down, Right, Up.

Disco mode
While playing the game, press L1, Left, L1, Left, R1, Right, R1, Right.