In order to get this on Outpost you must first take the tape from the Captain during the Defense mission. After fighting off waves of mutants and passing out, you'll wake to find your allies all dead save the Captain, who is wounded and barely holding on. Take his tape, and once you reach the Outpost mission, climb to the top of the building and look for a small shack. Inside is a tape player. Interact with it to broadcast the message and unlock this achievement.
I've created a full Enlightened playthrough video showing almost every Moral Point in the game as well as pointing out items of interest, such as this achievement.
You can see the Defense mission with all items of interest and collectibles, including pointing out where to take the tape, at the
1:13:54 mark in the video. Outpost immediately follows Defense, both in the game and in the video.