View Solution

This achievement is easier to get with Blue Sun Corporation, as they can buy new applicants.

Setup a colony where you can export rare metals automatically. Once you have enough money, spam the 'buy applicants' option until you can fill your rockets with vegans. You can check how many vegans are available with the quirk filter.

Apparently, the game checks for this achievement when one of your colonists get a new trait, so you may have to wait a little after you reached 200. The morpheus project or other technologies that give new traits may speed up this phase.

Good luck