You know we could win a free game because of it with the steam sale so... Starting with alchemy seems to be the best way, but I'm not sure. This is as much for other people as it is for me (I want to help friends do it fast, who already have the game)
Alchemy. You should be able to knock it out inside of the first floor...unless you're not cuddly enough with the RNG God to get a Grog, that is.
You should be able to buy grog from the drink vendor for like 67 gold. There is almost always one in there. I got the achievement in the first 5 minutes of starting my new character today.
Haha, shows what I know! I all-but ignore vending machines unless the phrase "Crafty Crafts" is featured prominently on them.
Burglary, Alchemy, Werediggle, and a pile of melee procs. Restart the game until you find Grog in the opening Drink machine (if you get lucky and steal it, so much the better.) Use the Aqua Vitae you get from starting with Alchemy, a couple of Diggle Eggs (put your levelup points into Werediggle so that if you magically come up with a level with no Diggle Nests, you can poop your own), and that Grog from the opening vendor if you didn't find one elsewhere. Presto.
That steam sale/achievement thing must be boosting sales like no other. Another forum I frequent almost all the steam users now have DoD!