Cheats:
At the main menu, hold both triggers and press Left, Up, Down, A, Right, B, Start. This will bring up the code entry screen. Now enter the following cheats.

SUPERMECH     Invincibility
WHERESMAX     All models are awards
WEWILLWIN     Level select
MULTIMAYHEM   All multiplayer levels
SPACEFOLD     Gunpod refresh faster
MARSBASE      Missiles refresh faster
MIRIYA        Gunpod and missiles refresh faster
BACKSTABBER   One shot kills
SNIPER        One shot sniper kills
MISSMACROSS   All paint schemes 
FLIPSIDE      Upside down mode
CLEAR         Turn off codes

Invincibility:
Go into Training mode, pick the Veritech Fighter training, shoot down only the first two targets, then quit the game. Now go into Story mode and you'll be indestructible no matter the stage or style of fighter that you choose.

Thanks to Revolution readers -TroJax-, Aaron Ortega, and Ginger!