Enter the following codes at the Title screen, then load a save or start a new game. Now pause during play and select the cheat option at the level select menu.

Invincibility:
Press Y, B, B, X, X ,X, Y, Y, B, B, B, X, X, X, X, B, Y, X, X, X, B, X, Y, X, X, B, X, X, Y, X, B, X, X, X, Y.

Level Select:
Press Y, Y, Y, B, B, X, B, Y, X, B, Y, B, Y, B, Y, X, Y, Y.

Secret Level:
Press Y, B, X, X, B, Y, Y, B, X, X, B, Y, Y, X, B, Y, B, X, X, B, Y.

View Credits:
Press Y, B, X, Y, Y, B, X, Y, B, X, Y, B, B, X, Y, B, X, Y, B, X, X, Y, B, X.

Thanks to Revolution readers StupendousMan, Ronny B, Viktor and j_j_j!