If you're like me and you can't catch plague no matter how many times you get hit or how many bodies you search, here's a guaranteed way to get this achievement:
Playing as Arthur, visit the Apothecary shop in St. George's Holm and talk to the guy at the counter, Stewart Adams. He'll give you a quest called A Sucker for Science (I never had a yellow quest marker for this). Complete this simple quest then come back to him and he'll give you another quest called Mother's Little Helper. Once you've dealt with Mrs. Chaney in this quest, go in the adjoining bathroom and pick up the drugs called Altered Formula Dexipam. Inject yourself with these drugs and tada, you've got the plague. Then use a Phenocycline Jab and job done, achievement unlocked.