This achievement is very easily done while playing on casual and adding 3 bots. They will revive you constantly and kill zombies very quickly.
You simply may not open the door to the catwalk after turning on the power. The bots will not open this door either but I would recommend keeping them away from there just in case.
You should use your special weapon (overkill is recommended) as often as possible. You can also use traps found in the workshop on the right side although notice that the bots will frequently walk into the trap and go down.
Luckily the mystery box will also always spawn on the west side of the map so getting a gun that can carry you to round 20 wont be a problem.