I thought I'd offer this method, which I see that no one else has posted yet. I used it and got the achievement on my first try. I honestly think that this is the easiest and most hassle-free method, even for getting through the mansion.No Time Bomb, no Paralyzer, no excessive use of Leroy required.
The only things that the video doesn't cover and that I'd recommend doing are putting it on Easy difficulty so that the last zombie does not start sprinting, and also to play with at least one other person so that they can hold the zombie. Other than that, the video covers everything.
(Sorry to those who prefer written guides; I figured it would be easier for everyone to see the video instead of having me describe the method in the video)
By following the video, you'll also get:
[Credit for this method and the video goes to S1pperyJim on YouTube.]