In order to get his attention so that you get the recipe, you have to destroy the thing most precious to him (well, and maybe to you too)--the large kegs of brew. When you first enter the bar through the steps, take a left and you'll find an empty room with some kegs you can destroy. You'll destroy three of these and Blackbreath will come running in with some cronies who are also in a very bad mood now.
Blackbreath and the cronies are elites. The strategy is simple: Have your tank bash the kegs and everyone stand back in the NW corner of the room. Your tank can then charge/attack Blackbreath to draw aggro. Stomp, or whatever is a good idea just to get everyone hitting the tank. The fight is fairly straightforward. Use any crowd control techniques you have (sheep someone, for example). Blackbreath has a lot of hit-points, so whether you choose to or not, you'll probably take out the cronies first (and in this manner, reduce the damage your tank is taking).