As soon as you start the Ground Zeroes main mission, you'll see a little zone crammed with white tents to your left. The prisoner is confined in a small shack around the northwest corner of this fenced-in area. Be aware of any guards about you, especially the one in the tower controlling the spotlight.

As long as you tranquilized a majority of the enemies in the fenced-in vicinity, you should be able to designate a safe landing zone for the helicopter at the cliff where you began the mission. Put the prisoner on the chopper and the achievement will unlock.