The only arena that has all 6 different types of zombies is Arena C, the swamp map. You should get a Walker, Infected, Floater and Suicider in the early rounds. On round 11 the first Ram will appear and round 14 will hold the first Butcher.
You don't need to kill a Thug in order to get this achievement, just all of the above types. If I remember correctly a Thug doesn't even count towards this achievement.