To be honest, I have never heard of anyone calling themselves monster hunters. I personally am not a fan of most "hereditary practices", as I feel most of it is just fluff. However, there are some practices that could be considered "monster hunters".
I only know of a few traditions that have incorporated "the hunt" into their practice. Especially those who are followers of Cernunnos, but some worshipers of Artemis i know of also incorporate it as well. These types of hunts can be either physically or spiritual. The spiritual hunt is where you would see the hunting of mythological creatures. But it tends to be metaphorical and more as a form of worship than just going out and shooting a dragon.
There is a coven on tumblr that is known for their spiritual hunts. Even to the extent that all of them have spiritual familiars that are hunting dogs, that they use when following Cernunnos. But I don't go on tumblr enough to know the details. Perhaps look around there?
I hope that is what you were asking! Sorry that got a little wordy.