When you knock off a [Goliath's][1] helmet and the little terrifying David Lynch head comes out, they go berserk and attack everyone.  They level up by killing their former allies.

> Upon killing enemies, the Goliath will gain experience points and gain levels, becoming even more dangerous. A beneficial aspect of this is that the dropped loot will be better. At the GOD ith level, drops are greatly increased. 

An easy way to tell whether or not you've gotten it to a high enough level for the "Goliath, Meet David" achievement is if the Goliath has God in its name.


  [1]: http://borderlands.wikia.com/wiki/Goliath