Firstly, for this achievement level up until you unlock the Double Lariat skill move, because that makes this achievement easy.
Head to Seon's Food and Stuff in the North Plaza, unequip your weapon with
and then go to town on the zombies with the Double Lariat (
). If you need to heal, there's food all around, and if you want more kills head out of Seon's and there will be a massive horde just outside in the North Plaza. Keep doing that until you unlock the achievement.