For this, all you need to do is win a game with double the score, or higher, of your opponent.
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 play a really bad word that's two or three letters long. Then switch to your main account via Windows 8's 'switch user' function, and play a word of double the value, or higher, than the really short word you just put on your secondary account. Switch back to your secondary account, see the word come up, and then click resign. Switch back to your main account, check your 'played games', and the achievement will pop.