Infinite Continues:
On the Press Start Screen, Press Right, Left, Down, X, X, X, B, A, Y, B.

All Extra Options:
On the Press Start Screen, Press Up, Down, Left, A, A, A, Y, X, A, X.

Unlock All FMV Sequences:
On the Press Start Screen, Press Down, Right, Up, B, B, B, X, Y, B, X.

Battle Mode:
Beat the game on Normal to get Battle Arena mode.

No Limit Mode:
Beat the game on Hard to get No Limit mode.

Puck's Mini Game:
Beat the game on Easy to get Puck's Mini Game (Here's where the Japanese Influence is... *shudder*!)

Hints

Infinite Health Vials 
575F468100000005 

Infinite Credits 
600B69340000000A 

Infinite Grenades 
8ABBBCD600000005 

Infinite Hand Cannon Ammo 
5767468100000005
 
 

Thanks to Revolution reader Joeman, Luis Arroyo and Jordon Cahow!