Easiest way I found was to play Resistance Mode on the map Las Barricadas. At the very last checkpoint, once you've completed the objective, the dispatcher will advise you to leave the area and get to the tunnels to end the mission. However, a Goliath rolls out onto the street shortly before she does that and this is where you get the achievement.
I'd suggest playing on Easy and you should have the RPG unlocked along with several handmade explosives as the Goliath can take quite a beating before going down. There is an ammo crate at that checkpoint, and I'd suggest not using it until you've hit the Goliath with all of your RPG shots. If it still hasn't gone down, go refill and hit it 3 more times. That should take it down.