As the achievement involves any mode in Xbox Live, simply playing matches online, be it Ranked, Player or Global Colosseo will eventually net you the achievement.
However, if you have a willing friend or have gaming session partners who own SCV, you can shorten this time dramatically through the use of Player Matches.
Set up a player match with your partner, ensuring that you set the round limit to ONE round. From here, I recommend picking a small map to easily ring out your enemies on. I suggest Mt. Fuji the Holy (the level with the raft), as it's both miniscule, and has no walls to prevent ring outs. From here, choose a character that has easy ring out capabilities and repeatedly ring out your opponent. (For example, Raphael's Vertical throw has good distance and ring-out capabilities).
For those who just don't know who to use, I can recommend Aeon; just repeatedly use 66K (or Right, Right, Kick) to do a charge which has great knockback distance.
This will also net you significant player points, meaning you can gain progress towards the Player Level achievements using this method, as well as the Hands of the Abyss achievement for multiple ring outs.