This is exactly like the achievement for King of the Hill.
Go into your online multiplayer menu, and go Player Match > Survivor, you'll be added to a cue of challengers for a Survivor/King, and whoever wins each match takes over that role. All you have to do is wait you turn and try to defeat the Survivor.
If you have a friend on the game, you can start these matches via the Private Match screen and just throw the matches for eachother.
Unfortunately, if you don't have a boosting partner there's no real easy way to do it. You'll need to either get good or hope you get lucky.