Invincibility:
Pick CREDITS in the options prompt then push L1, Triangle, Up, Down, Circle(2), Triangle, Square, Right, Square.

Disable enemy AI:
Pick CREDITS in the options prompt then push L1, Triangle, Up, Down, Circle(2), Left(2), L1, L2.

One hit kill with firearms:
Pick CREDITS in the options prompt then push L1, Triangle, Up, Down, Circle(2), Triangle, Square, Down, R1.

Expert mode:
Pick CREDITS in the options prompt then push Down(3), Triangle, Down(3), Square, Left, Right for more challenging opponents.

Instant puzzle solution:
Pick CREDITS in the options prompt then push L1, Triangle, Up, Down, Circle(2), Down(3), Up.

Avoid damage:
Hold R2 and any direction on the D-pad and no enemies will be able to hit you.