Ideally, go for this achievement right at the beginning of the game when losing popularity doesn't matter, considering you're starting with 0 popularity anyway. If you're already into the game, I recommend keeping this achievement for last, so you won't suffer from the loss in popularity by doing it the fast way.
Assuming you've been catering to "nice" customers the whole game through, your reputation is probably around +100. If so, you won't get any "evil" customers, which are the game's main source of decreasing your reputation. The only other (and fairly quick) method of getting your reputation down quick is simple: just turn down any "nice" customers you get. Your popularity will get tanked from doing this, but considering how rare "evil" customers are at max reputation, you don't have much of a choice. Keep sending nice customers away, reducing your reputation by around 2 for every customer, until you get the "evil" customers. Be sure to serve every single evil customer that comes into your shop. Evil customers are an amazing source of decreasing reputation, with some of them decreasing it by up to 20. Eventually, when your reputation hits the negatives, you'll only encounter evil customers. Just keep serving every one of them to the best of your ability until you hit -100. After that, if you still need the Good-natured achievement, just do the reverse. Deny service to evil customers, help nice customers to the best of your ability.
TL;DR:
Deny service to every single nice customer, give the right potions to every single evil customer.