Wow, thanks for all the input guys!
I do live in Alberta, and will review the regs before I go and try and take down some of these big rats. I was interested in the minimum calibre, I guess out of a need to be somewhat humane. I don't want to find out they have super thick skulls and my .22LR bounce off.."ping ping ping!" But from what you have all told me, just about anything will work for them, obviously within an effective range at the proper target on the animal. I may even get my 870 before then, who knows. If it comes down to it, I will use my 10/22. I don't beleive the pelts are worth anything except their obvious use as a wicked halloween costume.. If I find a monster beaver maybe I will take his pelt, for the memories.
Now, Ive been hearing that most of their activity is nocturnal? Anyone have any sort of tips that can help me get them during the day? Somewhere in my head I am thinking of a bag of fireworks (screecheroos and the like) and some very pissed off beavers.