Liberate an outpost without triggering an alarm.

You will get this achievement automatically, without doing anything special, after completing the Kick the Hornets Nest mission. One of the best and most fun missions in the game.

That said, shoot the alarm box(es) at the outpost. This will disable them. Best done with a sniper rifle, one with a silencer works best. Then take out each enemy from a distance.
Alternatively you can shoot the cages with animals in, not all outposts contain caged animals. They will escape and do some dirty work. I got the achievement through this method.