Hard mode:

Successfully complete the game on the normal difficulty setting with a "B" or higher rank to unlock hard mode.

Short mode:

Successfully complete the game on the easy or normal difficulty setting to unlock short mode. Load the cleared saved game to toggle short mode.

Lv3PK mod:

Successfully complete the game on the hard difficulty setting with an "S" rank to unlock Lv3PK mode.

Alternate ending sequence:

Successfully complete the game on the normal or hard difficulty setting.

Thanks to RamirezXsJ