This guy is like a mustache-twirling cartoon villain. The only problem is, he can actually cause people very real, non-cartoon pain, and when he fires bullets, they hit their target. On one level, Tenorio serves as the embodiment of revenge. It's pretty much all he talks about. Here's a little gem: "For that I curse you! I will see you dead! And you, Narciso, I swear to kill you!" (12.480-482).
Tenorio is all about exclamation points, and in the end he makes good on his word. He ambushes Narciso like a full-on coward and shoots him, and he kills Ultima's owl, which is just like killing Ultima herself.
While Tenorio serves as a direct antagonist to Antonio (they run into each other several times throughout the book), he also antagonizes Antonio on a level that goes beyond the physical. Antonio's doubts in God stem in part from the fact that he cannot understand why a man as evil as Tenorio manages to go unpunished by God.
In the end, though, Tenorio gets his in the form of a bullet from Uncle Pedro. However, by that point, Antonio has already begun to think about creating a "new religion" (22.160), that could account for the existence of bad dudes like Tenorio in the world.