You just have to complete 100 matches (not win); but you must capture at least three 'rings' during the match. Since this Annex achievement can now be done via Koth and Blitz gametypes (which are only one round) you have to be on point with ring captures. Annex is very similar to the King of the Hill gametype. In Annex the rings always spawn at a weapon spawn point.
Easy way: Using a second controller logged in as guest, you can create an Xbox Live, private Blitz match. Have the settings at one round, 180 second win timer. It's you verse your bot. So just cap the points and win with ease. This can be done anywhere, but use a smaller map to make things go quicker. Using this method, a one round match should take no longer than four minutes each.
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 now 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 must cap at least three rings during the match or it will not count!