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Walkthrough
At the start of this quest, you'll chase the Beast of Toussaint to a warehouse in Beauclair (#1). Inside, the two of you will exchange pleasantries and then the battle will begin. The Beast is a vampire, so you should use
Black Blood and
Vampire Oil right away. After that, you'll just need to damage the Beast as best you can. He'll teleport around and hit you hard, but you should be able to get some strikes in on him and then dodge away and heal as much as you need.
Once you've done enough damage to the Beast, you'll earn 1000 xp, and a cut scene will start up where the Beast will maneuver around for a deathblow -- only to be foiled by a fellow vampire named Regis (who Geralt knows from the Witcher books). The Beast will get away, but Regis will explain a few things about him -- that his name is Dettlaff, that he saved Regis' life, and that he doesn't do anything without a good reason. Regis will even compare him to you.
At the end of the conversation, Regis will agree to help you find Dettlaff, but only to reason with him, not kill him. Since your job is the stop the killings, you'll agree to this.
1 - Warehouse