God Hand - PS2

Fighting Ring challenges:
Beat the first stage.

Bonus Arena Challenges:
Beat the game to unlock Arena Challenges 41 through 50. Beat those to unlock Arena Challenge 51.

Hard mode:
Beat the game under normal difficulty.

Chihuahua Race:
Beat Stage 3, then talk to the guy in the shop.

Alternate costumes:
Beat the game to unlock the Carnival, Devil Hand, Karate, and Olivia's Bunny Girl costumes. They can be obtained by starting from Stage 2 then talking to the new NPC in the shop.