Invincibility:
Hold Select and quickly press Triangle(3) at the main menu. Then, press Triangle, Circle(2), Triangle, Circle, Square, X(2).

Level select:
Hold Select and quickly press Triangle(3) at the main menu. Then, press Square, X, Square, Triangle, X, Triangle, Circle, Square. Begin a new game, then hold Select and press Left or Right at the mission introduction screen to choose a new starting level.

Super gun:
Hold Select and quickly press Triangle(3) at the main menu. Then, press X, Circle, Triangle, X(2), Circle, X, Square.

Invisibility:
Hold Select and quickly press Triangle(3) at the main menu. Then, press Square, Triangle, X, Square, Triangle, Circle, X, Triangle.

Overhead view:
Hold Select and quickly press Triangle(3) at the main menu. Then, press Triangle(2), X(2), Square, Circle, Square, X.