For this, all you need to do is Win 5 games in a row.
You can do this with the use of a secondary profile, as you do not require a gold membership to play Alphajax online (as it is asynchronous multiplayer, free download, and on windows 8, instead of the 360).
Login to your second profile on windows 8. Challenge your main account to a game, and before you put a word, click 'resign' in the bottom right corner. Do this five times. Switch user to your main account, check your 'played games', and the achievement will pop.