I had a few issues with getting this to unlock when I ignored all the enemies at the beginning. It isn't necessary for most people to kill the first enemies, but in my case I had to.
Go through the mission killing all the enemies along the way. Once you get inside the structure. Continue going through the mission for a little bit longer, and you'll come to another door. When you enter the door, there will be a ledge and a lower area below you with some plasma turrets and a few enemies. The cowardly grunt can be found under this ledge, but he will only speak once the enemies have been killed. After clearing the area, walk up to him to get the achievement.