Easy mode:
To get easy mode, die three times and then go to the Main Menu and select 'Tokuten'. Now go to difficulty settings and switch it to Easy.

Hard mode:
Beat the game on Normal difficulty.

Kick ass mode:
Beat the game on Hard difficulty.

Special bonuses:
Beat the game on any difficulty to get the Onimusha 3 teaser, the Scenario Route mode, Man In Black mode, and Team Onimusha mode.

Mind Twister mode:
Beat the game and get all paintings.

Leather outfit:
Beat the game with the rank 'Onimusha.'

Thanks to Revolution readers DaManP, Chase Hall, mike, G-bAbY, and Chase Hall!