For this you need to kill a GOD-liath (Fatal GOD-Goliath). For a Goliath to become GOD-liath you'll need to get him to level up four times. You'll know when he's leveled up as he'll do a small animation, gain some health back and his name will change from Goliath to Raging Goliath, Badass Goliath, Super Badass Goliath then Ultimate Badass Goliath and finally GOD-liath. The earliest i could find one were in the Frostburn Canyon during the quest "Hunting The Firehawk". You have to shoot his mask off, he'll then go on a rampage killing everything around him. The enemies will actually start shooting him and he dies quickly so what i did when i saw one i killed all the powerful enemies leaving few weak ones shoot his mask of and let him take care of the rest (you could also simply weaken the tougher enemies instead of killing them and then shoot his mask off), now if he's not level 5 by then there are plenty Spiderants around Forstburn Canyon and since he'll follow you it shouldn't be a problem getting him to one of the spawn points. It's best not to shoot him at all, you want him to have as much health as possible, since they aren't that hard to kill. Now once he kills enough enemies he'll become a GOD-liath. Just unload into him and once he's down there's your trophy.
This only unlocks for the Person that kills him.
Thanks go to dL KryZi from TrueTrophies sister site TrueAchievements.