I've found the easiest way to get this is to go to the Frostburn Canyon. You will encounter quite a few goliaths here, however, you'll find that they aren't very resilient, especially against enemies such as pyro nomads. I found that even with attempting to weaken the enemies shooting the Goliath, it would still die.
Then I came across a "Loot Goon Goliath". You'll easily be able to pick these out from the normal ones as they are much bigger than the normal Goliaths and they have a loot chest on their back. It seems to spawn one every time Frostburn Canyon repopulates with enemies. Typically I would find him wandering around the middle of the map.
The great thing about this guy (aside from loot of course) is that he is much tougher than normal goliaths, so you won't have to babysit him while ge fights the other enemies Once you see him, shoot his helmet off. After this, he'll become enraged and start all attacking everything. Simply kite him around to different camps and enemy spawn locations until he increases by 4 levels, becoming a "God-liath". Once this happens, you can start pumping bullets into him, getting the achievement once you kill him.
A couple notes to make:
1. I've only been playing co-op, so it is possible he won't be there if playing alone. (thanks to InfiniteRefrain for confirming he does appear in single-player)
2. If playing co-op, only the person who actually kills it will get the achievement.
3. I am very confident this is the best way to do this. After trying several times and failing, I was able to do this 3 separate times just randomly going to Frostburn Canyon for various missions.
If you are down voting this, please leave a comment so I can improve the guide, thanks