Just got this finished. Mostly luck will get this achievement, except for the guide from XCVii007r1 (which was done very nicely I might add).
I finished with 2 other guys, we had 1 hobbler running around and when we felt we were ready (we had a feeling the Thief was coming out after the last zombie died during this round as the power had been turned on for a level before) we killed the last hobbling zombie to start the Extra Thief Round. Right after killing the hobbling zombie, he dropped the Death Machine. One of our team retrieved the Death Machine and the thief popped up to only be shot down in 1 sec from the Death Machine.