You can go for this while trying to get the invitation from Fela, if you accuse Greg of being the interloper, or you can get it during the drinking contest with Apollyon after the trial. After each shot, you have a cup that moves back and forth. You can control it to a degree with the left stick, and you have to place it on the stack by hitting
To win, you have to get above the line before your opponent does, which requires you to stack five cups. With each shot, the cup moves faster across the middle, so it gets trickier and trickier to get it on the stack, but take your time... your opponent will miss one or two, so you have a little bit of leeway as long as you don't panic.
If you break a glass, you can quit to the main menu and reload, and you'll start right at the beginning of the drinking game again. Be sure to quit right away... the game autosaves at the end, win or lose, and then you'll have to try to earn this with other drinking games (which are harder, and don't have as convenient save points), or wait until your second playthrough.