This achievement has become unobtainable as of 4-30-12 due to server being shut off for this game. Even though you could get this with 2 gold accounts on the same console you have to be connected to the EA servers to gain the achievement.
This doesn't have to be a public game.
Go to Play via Xbox LIVE < Create < Select game type: Scrabble. then select visibilty set to private. invite your boosting friend.
I just played original, so I don't know if the other game types go faster. but I used this website to help find wordshttp://scrabblefinder.com/solver/