I just got this title a little over a month ago. It has nothing to do with how long you stay drunk it has to do with drinking while already drunk to raise your addiction level to 10,000. Basically you want a measuring cup set to a small amount and just continuously keep taking sips until you get it. I want to say it took me a few hours to get it.
Edit: Just went back to check logs. It took 1.5 hours of filling measuring cups and drinking. I went about 10 extra minutes because the title message doesn't pop up on screen and you spam past it with all the filling and drinking actions. So start checking your titles window after an hour and a half or so.
Also be aware that after you will detox for a while, getting a shake and tremble message for every 1000 points of addiction you lose. During this time I read that if you were repairing something there was a chance of instead getting massive damage on the item. Didn't happen to me but I didn't risk it on anything important either, I just took it easy until it went away.