Cardinal Monticelso might be better at committing vengeance than being a priest—though it's not like that stopped him from becoming the Pope or anything. Technically, he's supposed to be on the right side: Brachiano is a pretty detestable character, and the Cardinal clearly wants to kill him. But, at the same time, he's a corrupt churchman—the kind of guy who owns a book listing known-criminals, many of whom are useful for aiding revenge. He publicly attacks Lodovico for being a criminal while simultaneously using him as the instrument of vengeance against Brachiano, Vittoria, and Flamineo.
Also, most readers will probably find Monticelso's speech against Vittoria a little crazy and bitter. He attacks Vittoria for being a "whore," stating:
What are whores!
Cold Russian winters, that appear so barren,
As if that nature had forgot the spring.
They are the true material fire of hell… (3.2)
This leads the French Ambassador to comment on Vittoria, "She hath lived ill," to which the English ambassador replies, "True, but the cardinal's too bitter." (Clearly, these guys are meant to represent the audience's own reactions).
When the Cardinal needs to, he can scheme for revenge with the best of them. He gives Francisco the following, cunning piece of advice, which helps sum up the crafty movements of his own mind:
Mont. …sleep with the lion,
And let this brood of secure foolish mice
Play with your nostrils, till the time be ripe
For th' bloody audit, and the fatal gripe:
Aim like a cunning fowler, close one eye,
That you the better may your game espy. (4.1)