Drink 400 sips of alcohol/hellcohol. That equals 40 full drinks fully drunk.
This is quickest to do during the graduation party, right at the beginning, since you don't have to watch a long bartending animation. Just camp in front of the drink table, hold the right trigger down to chug your drinks and refill with the A button.
Your progress is not carried over between playthroughs. If you start a new game, you have to start over.