Big Head Mode

Pause the game and press L1 + L2+ R2+ Down
Submitted by Alf

Invincibility

Pause game and enter Circle + Square + Right, Left + R1 + R2. If done correctly you'll hear an explosion.
Submitted by Alf 

Level Passwords

1st Moon XSXSSCSC
2nd Moon CXXTCCXT
3rd Moon CTSCSSTT
4th Moon CXXXTCTT
5th Moon XXSXSSTC