The monologue is the clearest sign of a criminal mastermind. Forget the deathtrap lair in a volcano, the piranha pool for disposing of substandard underlings, the secret rocket launching facility disguised as an inner city basketball court, the string of nuclear bombs planted under every hydroelectric power plant on the earthquake-fault-riddled west coast, and the custom built mobile luxury penthouse in a railway car that sprouts wings and can control the weather. What really, truly makes the villain is the monologue.
No other indicator of mastermindedness or villaininity is so clear-cut and character defining as the monologue.
If you want to make your evil genius stand out above the pack of NPC mook rabble, to tower head and shoulders over the trampled and betrodden remains of the disposable bad guys thrown into the path of the PCs, to present the impression of pure and implacable badass to-be-reckoned-with nastiness that will quake your players in their boots and let them know, in no uncertain terms, that this is the source of all their woes, then you need to compose a monologue of such awesome, such depravity, such unbridled insanity and in-your-face-ness, that your players will cower before its might and beg to be released from its iron grip once you have begun reading it.
Show them no mercy. This is the villain's moment. He's destined to be defeated anyway - there's no hiding it. But allow him this one perfect shining example of all that is right about his own deluded way of seeing how the world would be a better place if only everyone listened to his genius. But of course they don't, and therein lies the tragedy.
For a good monologue not only sets up the villain as the ultimate bad guy, but also provides the hook for sympathy. Because, damnit, he's actually right about some of the things he's saying. It really would be nice if everyone had a puppy, and people helped each other get the leaves out of their gutters, and anyone who parked in a disabled spot without a permit was summarily made to defend a goal for 20 minutes against a wheelchair rugby team. It's just the methods that are wrong: You can't give everyone a puppy by detonating the entire Pacific Ring of Fire in an attempt to drain the ocean and uncover the lost city of Atlantis so you can retrieve their lost knowledge and become ruler of the world. (It's not in the Pacific, for starters.)
So use your monologue to impress all of these things on your players. Don't let them interrupt. Or your villain might come across as goofy as Count Dookû here.
Count Dookû: You arrogant Zhedi swine!
Count Dookû: Zis Zhango Fett, do you even know 'ow 'e is fahnancing zis clone army?
Obi-Wan: How he is... what?
Count Dookû: Fah-nanc-ing.
Count Dookû: 'e 'as been, 'ow you say... embezzling funds from your precious Zhedi Council.
Obi-Wan: What? But that implies he has an inside contact...
Count Dookû: Ah 'eard 'e 'ired a shapeshiftair.
Obi-Wan: The assassin! Of course.
Obi-Wan: She could get into the Jedi Archives too!
Count Dookû: At last you begin to see. We 'ave enemies on all sides.
Obi-Wan: What's this "we" business?
Count Dookû: Do you not, after 'earing me out, want to 'elp me foil Palpatine's evil scheme?
Obi-Wan: Let's see.
Obi-Wan: You stole the plans for a symbol of peace.
Obi-Wan: You're allied with (a) a known megalomaniacal warlord and (b) a criminal sociopath.
Obi-Wan: You have not one, but two, armies at your disposal.
Obi-Wan: You've captured me—unfairly—and are holding me with no means of escape.
Obi-Wan: And you're monologuing.
Count Dookû: Ah am monologuing?!