Once Cartman becomes an available buddy, set him as your buddy. In battle, you must use one of his fart attacks to kill an enemy. Repeat this on 20 enemies cumulatively to unlock the achievement. His best fart attack is his ability on the right of the wheel. It is an AoE attack that hits all enemies with fire, meaining you're more likely to kill multiple enemies with this attack at once. You'll unlock Cartman while the zombies are still present, and this is the best time to farm this achievement, as a lot of zombies are weak to fire.