You can acquire Dire AIDS from the dire wolves or snakes in Canada. Let them attack you until the game tells you that you acquired it. Don't remove it at the clinic. Simply finish the game with it and you'll unlock the achievement. The Dire AIDS doesn't affect you outside of battle once you have it. In battle, however, you will lose some health after each turn. There have been reports that it will eventually be removed after a certain amount of time. I recommend making a save after Canada when you're ready to go to Clyde's fortress, letting a dire animal bite you to give you AIDS, then go finish the game.
This can be paired with "Face Hoff" and "Two Girls, One Stick" to get all three achievements simultaneously.