Just as the description says: Complete a game in the Supply Raid mode on the maps Wharf, Capitol, Water Tower or Coal Mine.
Just as with any game with Multiplayer Achievements these days: It can be quite tricky to get a game going as the DLC maps aren't played a lot on the PS3 (as of right now - Okt 2015) and getting the right game mode on the right set of maps is purely based on luck (or determination).
Chances are you'll get this while randomly listing for a game, that's how I got this today. You don't have to explicitly list for DLC maps (I would actually advise against it), the maps pop up for a vote in regular listings as well as all players have access to them.
Unfortunately this can't be done in a private match.