When you progress to the fourth level of the dungeons under Torchlight a cutscene will trigger and Brink will be transformed into Brink the Corrupted.
You should treat him like you would any massive character. Simply spam your attacks and use your skills often. Don't be shy on the potions.
I've only played as the mage but i used his "ember shield". This absorbs damage. I would suggest casting that and after a few good hits (or every 30 sec.) re-cast it. You'll have him defeated in no time without worrying about dying or wasting potions.
All in all he is the first boss, as such he is very easy. His main attacks are a hard hitting melee, a lightning attack, and exploding crystals that materialize in front of you.
-Simply keep your distance and none of these attacks should be an issue.
Lastly, if you played the demo and beat Brink already then the achievement will not pop, even after you've completed the entire game. You have to create a new character and replay the quest and defeat him again.