You must shut out the opposing team during any given round. With this being added to public matches; the Koth and Blitz game types are only one round. So you must blank the opposing team for the entire match. In Annex the rings always spawn at a weapon spawn point.
If you don't have a second controller: You can play online in an Xbox Live private match with a second person and exchange wins. Or if the second person has a second controller, you can both be on the winning team against an idle bot.
This can be done in social or competitive matches, as the achievement description does not specify. So jump into your favorite ring-based game type and blast away. Remember, you can't allow the opposing team to score a single point or it will not count!