When you spawn 2 players are randomly chosen as traitors. This is announced to you and you have a red triangle icon beside your gamer tag. Search for the other player with the matching symbol (you are the only 2 that can see eachothers').
Preferably craft a weapon/tool quickly. I always prefer to be an axe murderer myself. Then attack this character in isolation. (In public you will attract attention and you might end up being beat down.)
The achievement should pop after the deed is done. Now you can switch clothes with the corpse to work towards another achievement and loot the body for any materials they might have been carrying.
Hope this helps and good luck!