This is easily obtained by completely ignoring the letters A, E, I, O, and U.
Words such as Why, Spy, Gypsy, Lynch, Nymph, etc... all work towards this achievement. Whenever you see the letter Y, do not use it until you see enough letters to make a word without a proper vowel. Luckily you only need 3 of these for this achievement so you should earn this in no time and may even earn it without thinking.