After beating the game, start a new game with @TREVOR as your name.
Boss Rush Mode:
Defeat every boss in the game including both of Dracula's forms, and both of the optional Legion battles. Once this is done, you can go to any warp room and enter the boss rush mode by sitting in the chair.
After beating the game, start a new game with @CRAZY as your name.
Once you beat Crazy Mode, the Moebius Brooch will be available in the shop. Equipping this item allows you to do special moves without using hearts.
First you will need a Lament of Innocence save file on your Memory Card. When you start the game in the Abandoned Castle stage, go around to the outside of the castle to find the Moai Statue. The statue is worth a lot of money at the shop, or it can be used to replenish your health.
After beating Boss Rush Mode, the music box should appear in the warp room. With this item, you should be able to access the Sound Mode Option to play various music from the game.