Here's a video guide if you prefer
Requires you to let a Goliath level up 4 times (Fatal GOD-liath) before killing him.
Best area to do this on would be “Frostburn Canyon”.
Watch out for Pyros who do heavy damage to Goliaths and make sure to damage surrounding enemies to allow the Goliath to get easy kills, also look out for barrels and explosives try shooting them when your Goliath is at a safe distance.
Having a character with elemental perks or a shield with elemental damage will make it hard to control the damage you cause to the surrounding enemies, I would advise using a character without those type of perks or shields.