Quarrel

Go to the challenge called the Battle of the Giants, you can make 3 anagrams and you will get the IQ of 200.

You start with 8 people on your tile and can make an anagram with a solver such as these: http://grecni.com/texttwist.php?query
http://homepage.ntlworld.com/adam.bozon/scrabble.htm

The other way to do it is to play normally and maximise the score for each play you make, so using your highest value tiles to maximise your score.

Good luck trying to do this aggravating achievement without an anagram solver!

Note: This is a suggestion for anyone who wants to get this achievement without relying on pausing and using a website to tell them the answer. If you prefer to do it that way, it's fine by me, but if not then read below.

Word IQ isn't actually based on making anagrams, it's based on your scores on each battle vs the maximum possible score with the letters you had. Thus it's much easier to get a perfect Word IQ when you're dealing with short words.

I did this in the first Showdown match against Dwayne. You need to attack him four times, twice you have 3 letters vs his 3, twice you have 2 letters vs his two. It should be pretty easy to find the best scoring combination of 2 or 3 letters, and it's all over very quickly so if you don't get it you can replay it. My average word score was only 8 points, but IQ was 200.