To access the debug mode menu, press Plus + 1 + 2 at the title screen. In debug mode you can change characters, weapons, and stages; and access the sound test and invincibility.
Plissken:
Complete the game on Normal to unlock Plissken.
Tsugu-Min:
Complete the game on Easy to unlock Tsugu-Min.
Nightmare difficulty:
To unlock Nightmare difficulty, complete the game on Hard difficulty. In Nightmare difficulty, enemies will shoot a blue ring after they are killed.
