When you're in the Stray Sheep bar you have the option to drink various liquor. Just sit down and press X until your drink is empty. The starting drink should be the Cocktail, so you'll receive a piece of trivia. Listen to one every night and the achievement is yours.
Note: You can only hear one per drink every night. So you can't just down a bunch of Cocktails to get this quickly. Just remember to drink it each night.