Antagonist
Character Role Analysis
Ferdinand and the Cardinal
This is pretty straight-forward: these Bad News Brothers are bad; real bad. They relentlessly try to control their sister, and when they can't they set out to kill not just her, but the entire family she's created with Antonio. There's literally nothing good about these guys. Haters to the front.
Bosola
Bosola's an antagonist for the obvious reason that he, you know, works as a spy for the bad guys and eventually kills our good guys, but there're other reasons, too.
One of the things that probably drove you crazy about Bosola is that, despite being arguably the most morally open-eyed character in this play, he works very hard to do what he believes to be morally wrong. Ferdinand asks Bosola to kill the Duchess, and even though Bosola knows the brothers are bad guys and he knows that Antonio and the Duchess are decent folks, he takes all that knowledge and he does it anyway. The contradiction that makes Bosola so interesting is also what makes him a villain—right before he dies he describes himself as "myself, / That was an actor in the main of all, / Much 'gainst mine own good nature" (5.5.83-85).