Achievement Name: KKK Hero
Description: You defeated the High Jew Elf Kyle in battle.
Guide: After you recruit the goth kids you will be given two chances to choose your allegiance - Cartman and his humans or Kyle and his elves. The first choice will be in the form of a mission that tells you to go to each one's respective base and talk to them to choose their side. This is NOT the one that will decide which achievement you get, it simply decides which side you will fight on in the upcoming battle.
At the end of the battle you will be standing between Kyle and Cartman and given the choice again. This is where you choose which achievement you will get. Turn and hit one of them to launch a battle scene. If you choose to attack Kyle, then beat him in the following battle, this achievement is yours.
It's worth noting you can also do a manual save just before this fight, and simply reload from that save point to battle the other, so that you get both achievements.