A goliath turns into a GOD-liath after leveling up four times, so be sure not to kill him before that.
Remove his head and try to debilitate the enemies around him so he doesn't get killed before leveling up.
I was able to unlock this achievement in Tundra Express. There are many larval varkids that are easy to kill so simply run around the varkid hives until your goliath reaches godliness. Then kill him without mercy.