If needed, the best place to grind this out is level 1, Ingleton, playing by yourself. You have to kill at least 50 and then 750 zombies in round 1 and then 500 more in round 2 to progress. Add collateral damage from rounds 4 and 5 and you are looking at around 1500 kills per run in about 10 minutes. You can either die at round 4 or finish the level, but do not quit as you'll lose your progression.
To make things go faster, remember to use the Rollerhawg in the graveyard in round 1 (go left after you crossed the blue "Walk" line) and the Turret Car in round 2 (get inside the garage as you break the door).
Character you use while on foot pretty much don't matter. You will have to use everyone anyway if you're going for all achievements.