This achievement is given for beating the game on 'Hardcore' difficulty. You must start a new campaign with this difficulty selected - you cannot choose it from Mission Select.
To unlock this difficulty you must first beat the game on 'Hard'.
In this mode, the difficulty is turned down to Normal but with _all_ checkpoints removed. If you die or fail an objective (anything that brings up a 'Retry?' screen) you are returned to the beginning of Mission 1: 'Unintended Consequences'. Think of it as an analogue to 'New York Minute Hardcore' in Max Payne 3 but without the timer.
The game saves this flag the instant you die or fail an objective, so dashboarding before the 'Retry?' screen comes up to stave off the reset will not work. However, if you are willing to deal with some tedium, you can guarantee unlocking this achievement for yourself.
At the start of every mission, after the initial checkpoint save icon disappears, dashboard out. Copy your Medal of Honor save (titled 'Profile Save Data'' on your Hard Drive) to a memory stick, and return to the game. If you die or fail, just replace the save file on your hard drive with the one you backed up. You will need to replay the mission you died on, but that is obviously far better than replaying X% of the game.
This will pop as soon as you shoot the Cleric in the head at the end of the last mission 'Shut It Down'.
As a reference, I managed to play the game on Hardcore in one sitting using this method in about 5 hours.