This achievement can easily be done solo as you can see in the video guide below. The Goliath almost always spawns on round 8 when your playing with 3-4 players but for me on solo it spawned during round 9. You want to get in the Goliath and then hunt down the zombies and simply melee them with
. This must be done in one game, you can not get 5 in one game and 5 more in another all 20 need to be done in one game.