Complete the game to unlock Boss Rush mode, Sound Test, and New Game+ options.
Hell Flame Soul move:
Beat the game as Soma in Hard Difficulty to unlock this move.
Have the GBA game Castlevania: Aria of Sorrow inserted in your DS when starting a new game. You'll have the Rare Ring in your inventory.
Alucard in Boss Rush mode:
Beat the game as Soma with a 100% completion. Also complete Julius mode. Then, at the Konami logo, press Up, Up, Down, Down, Left, Right, Left, Right, B, A at the Konami logo. When Konami logo appears again, press Up, Down, then hold Up until the sound of a door opening is heard. Enter Boss Rush mode to play as Alucard with the Alucard Set.
Thanks to Revolution reader aranel!