Select the "Showdown" encounter (Chapter 20) from the main menu, and play it on the Explorer difficulty. After killing the first three enemies in this area, four more will spawn close together on a rock. There is a rocket launcher sitting on one of the boxes in this area. Pick it up and shoot the four enemies after they jump down the rock. Aim at the enemy that carries a rocket launcher, as he has the strongest armor. This should easily kill all four of them. If you do not get it on your first try, simply restart the checkpoint and try again until you get the "Boom County" trophy.