Unlock Hard Mode
Beat the game once to unlock Hard Mode.

Unlock Legendary Dark Night Mode
Beat Hard Mode to unlock Legendary Dark Night Mode.

Unlock Super Dante
Beat Dante Must Die Mode to unlock Super Dante. With this, you can transform into a devil, and use magic indefinitely.

Unlock Dante Must Die Mode
Beat Legendary Dark Night Mode to unlock Dante Must Die Mode.

Unlock Easy Automatic Mode
Clear any mission from 1-3 using continues, and there will be an option at the start of the next mission asking if you wish to change to Easy.
Note: You cannot return to Normal once activated