NOTE that if you end a battle with your buddy unconscious, it will void the No Child Left Behind achievement.
You must be in a battle against at least 3 enemies. Let your buddy get knocked out while at least 3 enemies are still fighting, then knock them out by yourself. The easiest way to do this is to attack all 3 enemies until their health is very low, then let them knock out your buddy, then finish them off. I recommend making a save before doing this so as not to void the No Child Left Behind achievement.
The easiest places to do this are against the rats in Skeeters Bar, as they're very weak, or against a group of 3 kids in the neighborhood. To avoid killing the enemies, simply don't press or after you initiate a melee attack.
Tip: if you make Butters your buddy, enemies are more likely to attack him. That way, he'll take most of the damage and get knocked out quick, so you don't get frustrated with enemies constantly attacking you instead of your buddy.