AlphaJax

The quickest way that I found to do this was to select "local play" from the main menu.

Once in the local play game, play a relatively large word as your main profile, when play passes to the second "local user" profile, play the lowest scoring word you can find (preferably a two or three letter word).

It will be the main profile's turn again, if the main profile's score is double the "local user's" score, simply "pass" the main profile's turn and have the local user resign. Otherwise play another word as the main profile to make their score double that of the local user, then have the local user resign.

Note - If the achievement doesn't pop straight away, close the game, re-open it and the achievement should pop.

Just like Ttt19's solution, you can get this achievement in "Local Play".

Make any word you want, no matter how big or small the score is. Once its the "Local User's" turn, all you have to do is resign.

If at first you don't get the achievement you may have to restart the game; it should then pop up.

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.