Well, you could just rollover the Title's progress with your mouse and you'd find out that you need to be drunk for 1000 minutes. Dwarven ale tends to last 1-2 minutes each for me, after downing about 3-5 to start off.
Even though I threw this down as wrong The first time someone said it - Spiked Eggnog from the Christmas Event DOES keep you drunk longer than a normal Ale.
2 Minutes from just drinking ONE of them to be exact (no having to down 3 to get drunk).