This one seems like it would be easy. Bears should probably lose to the Prince of Darkness. There are, however, two drawbacks to the Delta Devils. First of all, their name reminds me of Delta Burke, which makes me sad. But more importantly than that is the actual depiction of the Delta Devil.
I'm not one to criticize, but I'm just not threatened by this green-skull-cap wearing Lord of the Underworld. Sure, he apparently controls fire, but that just reminds me of Pyro, which reminds me of X-Men: The Last Stand, which makes me weep. I have no doubt in my mind that a brown bear could take this guy in a fight. UCLA it is.
Brigham Young University Cougars vs. Texas A&M Aggies
I haven't met any students of an agricultural/mechanical school, and so cannot testify to the ferocity of Aggies. I'm sure they're more fierce than I am and wish them nothing but the best. However, put one of them in a cage with Felis Concolor and I'm guessing all of education in the world isn't going to stop the cougar from ripping his face off. BYU comes away with the win.
Drake University Bulldogs vs. Western Kentucky University Hilltoppers
I've already expressed my skepticism for the ferocity of bulldogs. I was worried that I was going to have to give yet another one to the bulldogs, because what the hell is a Hilltopper? Even their logo is some guy waving what appears to be a scarf. However, Wikipedia informs me that "Hilltopper" is a name for a horse that is used in fox hunting, and both because I can't figure out how a bulldog would go about killing a horse and a general superiority of the horse over the Canidae family implied by the fox hunting, this one's going to Western Kentucky. Plus, this picture made me inexplicably happy.
University of Connecticut Huskies vs. San Diego Toreros
Huskies are pretty solid dogs. They've got the pulling-a-sled-through-adverse-weather thing, though that's probably forced upon them and not their natural behavior, and the heterochromia thing is another point in their favor. Toreros, however, have lances and pointy sticks and swords. Sorry, Balko. This one goes to San Diego.
Purdue Boilermakers vs. Baylor Bears
There are a few mascots that are tough to see going down. Tigers are going to eat pretty much everything, as are bears. Bears, from what I understand through the experience of Timothy Treadwell, if you constantly mess with bears, ignore all safety precautions and anthropomorphize them to an absurd degree because you have no grasp on reality, they will eat you whole. It's hard to think of what could kill a bear.
Until you get to a train, which just runs it the hell over. Purdue wins.
Xavier Musketeers vs. Georgia Bulldogs
Thinking about it now that I'm almost done with the first round, I kind of think I should have painted bulldogs as incredibly fierce and tough in a fight, because it seems like at this point I could have had the entire Elite Eight be bulldogs. This one, however, is no contest. I don't even to have to suppose what kind of weaponry the Bulldogs' opponent have. They have muskets. Muskets beat dogs. Xavier with the win.
West Virginia Mountaineers vs. Arizona Wildcats
I grew up about an hour from West Virginia and am not going to make a joke about the residents thereof, because everyone I've known from WV has been fantastic and, besides, it's not as though I'm separated that far from them geographically. Still, I think any given mountain man from West Virginia could not only take a feral cat in a fight, but could skin it, eat it and make a nice hat out of it. West Virginia wins.
Duke Blue Devils vs. Belmont Bruins
Again with the not-very-threatening Devil depictions. The Duke Blue Devil looks more like a Batman villain than anything else, and I think I'd trust a bear to beat the tar out of him. Is this influenced by an attempt to appeal to Fark? Yes. But no one ever said a mascot bracket that has no relation to reality had to have integrity. Plus, Belmont Avenue is good times. Belmont wins.