Cheats
Unlike other games in the series, Red Dead Revolver doesn't feature any enterable cheats, however they can be unlocked in "Bounty Hunter" mode after completing the story.
Red Dead Revolver's cheats are unlocked by successfully completing challenges on specific levels during "Bounty Hunter" mode. You'll unlock this mode once you complete the game for the first time. It allows you to replay specific levels in any order, where completing them and passing the challenge objective will reward a cheat.
Once cheats have been unlocked, they can be activated from the pause menu. Enabling cheats does not disable trophies or achievements and there is no penalty for using them, meaning you'll essentially unlock the ability to make the game easier once you earn them.
Cheats can be used in the single player story or Bounty Hunter mode, but can't be enabled in Showdown Mode (local multiplayer). Using cheats in Bounty Hunter mode will make additional challenges easier to complete.
Unlocking cheats will unlock them for all "player profiles", so starting a new game with a new player profile would provide access to any unlocked cheats from a different profile.
Unlockable Cheats
Sad Stars
Whenever blood would be displayed, either when you shoot an enemy, or an enemy shoots you, a shower of colored stars with sad faces appears instead of the blood.
How To Unlock
In Bounty Hunter Mode on the mission "The Mine", you must pass the mission in under 3 minutes.

No HUD
All 2D graphical elements are removed from the heads-up display on screen. This includes ammo, health, deadeye and money displays, as well as weapon crosshairs and deadeye lock-on targets. It makes the game a LOT harder and unless you're trying to take screenshots, I'm not sure why you'd want to enable this!
How To Unlock
In Bounty Hunter Mode on the mission "Stagecoach", you must kill at least 40 enemies and pass the mission.

Bite The Bullet
All bullets deal a signficantly increased amount of damage. If you're hit by enemy bullets, you'll lose almost all of your health and will usually die in 2 hits. Most enemies will die in a single shot and bosses will take increased damage from each bullet.
How To Unlock
In Bounty Hunter Mode on the mission "Fort Diego", you must earn a combo of at least $300 and pass the mission.

No Distortion
All "camera distortion" is removed from the gameplay. Having tested this extensively, it's very difficult to see any change in the graphics at all. There is a suggestion that it removes the blur from the screen when you zoom in with your rifle, however, ultimately this cheat doesn't make any difference and is pretty pointless.
How To Unlock
In Bounty Hunter Mode on the mission "End Of The Line", you must get a combo of over $200 and pass the mission.

Infinite Deadeye
Your Deadeye meter will not decrease after use, meaning it can be repeatedly used without the need to refill it. You can still only lock in 6 targets with each use, but you can trigger it immediately again afterwards. The slow motion feature will continue forever until you manually end it by firing a shot or releasing L1 to stop aiming.
How To Unlock
In Bounty Hunter Mode on the mission "Battle Finale", you must kill Mr. Kelley in 1 minute. The time limit starts when Kelley gets back up after the duel and begins his rampage.

Golden Gun
All bullets you fire will deal a signficantly increased amount of damage. Most enemies will die in a single shot and bosses will take increased damage from each bullet, often allowing you to kill them in seconds. Enemy bullets are not affected and will continue to deal normal damage to you.
How To Unlock
In Bounty Hunter Mode on the mission "The Siege", you must pass the mission while keeping Jack Swift's health bar above 50%.

Invincibility
Your health bar will not decrease when being hit by enemy weapons, meaning you cannot be killed. You may occasionally still be stunned when hit by a critical enemy shot and you can still be knocked down, but you won't lose any health.
Invincibility doesn't work in duels, so you can still be killed if you're not quick enough on the draw. In some duels, you may be shot, but survive, allowing you to complete the shootout on foot.
Invincibility doesn't prevent your AI controlled buddies, or any vehicles you may be protecting from taking damage, so it's still possible to fail missions.
How To Unlock
In Bounty Hunter Mode on the mission "Fall From Grace", you must pass the mission in under 1 minute.

Cheat Unlock Tips
Invincibility is by far the best cheat to unlock and will help massively with all of the other objectives thoughout the game. As a result, you should play "Fall From Grace" in Bounty Hunter mode as soon as possible. Because you can play the Bounty Hunter missions in any order, you should definitely start with this one!
Once Invincibility has been unlocked, you should consider replaying "The Siege" to unlock Golden Gun then "Battle Finale" to unlock Infinite Deadeye. If you're struggling with "The Siege", try unlocking Infinite Deadeye first which will make things a lot easier.
Those three cheats will make the rest of the challenges, and your hard or very hard mode playthrough a breeze.
"No Name" / "RSTAR" Secret Cheat
When creating a new player profile, you're asked to enter your player name. If you clear the name and enter only a single space (represented by the ">" on the keyboard interface), then click on "End", the game will set your name as "RSTAR".
Contrary to rumors and misinformation I've read online, however, this doesn't appear to give any benefit to the player in-game. Nothing is unlocked early and no shop items are marked as "owned" before you've bought them.
Some items can be unlocked before you see them in the shop by completing levels or getting Excellent ratings which is where I think the confusion has come from.