To get this achievement, you need to perform a takedown on Burke without him going hostile. As soon as the cutscene with Burke ends, immediately take cover. Wait until the sniper on the left catwalk moves away, and then sneak past the mech until you reach a container with two ammo boxes in it. Turn around, and climb up on the metal support, then jump to the container. Turn right and jump down, and then immediately take cover. Sneak past the guard and the turret and go to the ladder, then wait until the heavy that is on the ceiling of the outpost that Burke is in turns away from you and climb up the next ladder. Perform a non-lethal takedown on the heavy (so you don't alert Burke and his guards) and then jump through the small hole below you. Burke will be staring out of the window, and you can just sneak up behind him and perform a takedown on him.