This is for the "King of the Hill" matches, located under 'player match' in the online multiplayer menu.
Essencially how these work is that it gets a cue of people lined up, then one person dubbed "The King" faces the next in line. The winner becomes king, the loser drops to the back of the line, and the king faces the next challenger. The goal then, is to become the king and keep beating opponents for as long as you can. When your turn comes up to face the king, defeating him (or her) will unlock this achievement.
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.