Before July 24, 2012, this achievement would have taken a minimum of four weeks to unlock if you start on a Thursday because you have to play five different Mutations, an old mutation would return for an encore week every four weeks, and then the permanently added Realism Versus could also be played.
You do NOT have to actually play through the rounds, all you have to do is join and start the round, to make progress.
The achievement can also be earned by using the developer console. By typing map mutation# you can start a map with any mutation you want and it will count as achievement progress. You have to replace # with a number for a specific mutation. A list of all mutations you can play can be found here.