Flying Mode
Press START at any time during the game to pause, then press L, A, Left, L, Right, Down, Down and unpause. Now you can fly into the air by holding the Y button.
Invincibility
Press START at any time during the game to pause, then press R, Right, A, L, Right, A, Down, Y and unpause. Now your character is invincible.
Stage Select
Press START at any time during the game to pause, then press L, A, Z, Y, Left, Right, A, Down, Right, L. A cheat menu will appear, allowing you to switch characters, access a sound test, enable the "flying" cheat or skip to any stage, including the bonus rounds.
