Invincibility:
Hold A + C + X and press Start when the phrase "Press Start" appears at the title screen. Fuu and Umi will be invincible when a new game is started.

Alternate introduction song:
Hold X + B + Z + L + R and power on the Saturn. Keep the buttons held until the opening sequence begins.

Remove text from new game screen:
Hold Left and press X at the new game/continue game screen.