All the maps:
DLC maps, including the day 1 edition "Ruins", are not needed.
You must get all of these in arena. When you matchmake it alternates which player gets to select the arena. If you do a custom game for arena, it will tell you what maps are in each one so you can pick and choose what you end up needing.
The fastest playlist (stolen from X360A - credit goes to "Metabolic x360a" and not the other solution here which is just a copy paste) is as follows:
Defense of Rome (Garden, Market & Castle)
Teamwork (Rabbit & Wickerman)
World Tour (Arch, Rabbit & Stronghold)
The Frontier (Black Forrest & Oasis)
Endless Hordes (Courtyard & Sandstorm)
It is confirmed in the comments you do not need to actually win the round. The achievement will unlock when you start your final map. Another comment says he tried the final map 3 times and the achieve popped when he beat it for the first time. So your mileage may vary.