You can start this achievement near the beginning of the game. You can start this when
You will be given the quest Lazarus Rising in which you must find 4 car parts. After you give him the parts walk away for a few minutes and do a quest or kill some zombies while he is repairing your truck. Return and your truck will be ready. Get in your truck and drive up and down the roads around the island running over any zombies you see. They will eventually respawn so just enjoy the game and it should come naturally.
As you are driving around mowing down zombies you will be making progress to: