Edit: There was a really awesome way to get cheat codes for the game, but they took it down. Sucks. :-(
As the description says, beat this level on Hard.
While the game isn't particularly difficult on Hard, there are some cheat codes that can help you if you get stuck.
1. Go to the Bonus Codes screen.
2. Go to the game's pre-order site: http://www.codemasters.com/jerichopreorder/index.php?shop=ga...
3. Copy/paste this as a pre-order code: AGEH-56JW-X2GB-DN1N-EGUT
4. On your Bonus Codes screen, you'll see a number. Enter it.
5. Enjoy your infinite ammo and faster health regen. The health regen definitely helps in the levels where you have to not die for the achievement.
There's a separate code for "Dominator Damage" that you can get by registering your game at www.codemasters.com/register. That further increases the damage that your weapons do.
Due credit to http://www.cheatcc.com/xbox360/clivebarkersjerichocheatscode...