This is a numbers game plain and simple. I got this in a long game to unlock all the miscellaneous trophies. Vegans will appear randomly through births or if you get a guru who has the trait (I've only ever gotten one guru in all my games though so don't bank on it). My population was well over 3,000 by the time I got the 200 vegans in the colony.
You can also bring in vegan colonists, but that will only help the process not be able to complete it. You'll need to let the population build naturally.