I believe the easiest way to get this achievement is to use the Scrabble board provided within this link: http://www.scrabulizer.com/
Simply enter in the letters used by the AI on to the game board (if they have a turn before yourself) and type out the selection of letters you have been given along the board. After each of the above instructions has been done and it is your turn, click the 'Get Solutions' tab on the right hand side of the screen and let the program work its magic and follow its instructions. Keep updating the board with the letters the AI are given and the letters you are handed out to replace the previously used ones until the game is finally over. I attempted this method several times and it has yet to fail me. Using this method I was able to unlock a lot of the other achievements, so it is highly recommended if you are looking to unlock them all.
PLEASE NOTE: The achievements required for beating the different difficulty levels of AI are not stackable, however if you continue to use this method, you will have no trouble at all.