At the start the Ground Zeroes main mission, look to your left to see the white tents in a large hole. The prisoner is confined in a small shack around the northwest corner of this fenced-in area. Make sure you tranq (or kill) the guard in the tower and the 2 near the fence so that you have an easily accessible escape route. Do your best to ensure that this is the only achievement you are doing on this level, that way you can focus on it and nothing more. Here is a video to help,
Credit goes to PowerPyx for the video.