Complete the corresponding Bounty Hunter challenges to unlock the cheats. You'll then see the cheats in the pause menu. Format below is cheat -> level.
Sad Stars: The Mine
No HUD: Stagecoach
Bite the Bullet (Enemies have golden guns): Fort Diego
No Distortion: End of the Line
Infinite Dead Eye: Battle Finale
Golden Gun: Siege
Invincibility: Fall From Grace

Hard Mode: Beat Story Mode
Very Hard Mode: Beat Hard Mode
Red Wood Revolver Mode: Beat Very Hard Mode (Manny Quinn, a wooden dummy will become the playable character. He has his own unique abilities).