Play in Magician Mode:
After completing the game w/ Nathan enter FIREBALL as your name when starting a new game.

Play in Fighter Mode:
After completing the game in MAGICIAN mode enter GRADIUS as your name when starting a new game.

Play in Shooter Mode:
After completing the game in MAGICIAN & FIGHTER modes enter CROSSBOW as your name when starting a new game.

Play in Thief Mode:
After completing the game in MAGICIAN, FIGHTER & SHOOTER modes enter DAGGER as your name when starting a new game.