Once in the Radio Room, you'll need to hack the broadcast in order to stop it. Then a large group of enemies will attack you, including at least 2 heavies. I used a health kit just before I hacked the broadcast, as I for some reason failed it the first time. Then I killed off all enemies and the achievement popped upon leaving the building.
I suggest to just camp in the broadcast room and take the enemies off from a distance, while moving back and forth from cover. Obviously, go for this on the easiest difficulty setting as there is no difficulty related achievements in the DLC's.