I think the coolest trick is to try to get the reader to sort of like the villain, in-spite of themselves. To return to Hannibal Lecter: although he was monstrous and frightening, he was charismatic. I guess the same could be said for The Joker. So, give them some redeeming qualities too, rather than just vile through and through.
This is how I handled the introduction of the villains Nick and Leo in my MS. For context, Alex has just murdered a man called Yorick for them:
Alex is in an office in Manchester. Nicholas is standing by one of the tall windows, bathed in sunlight, looking saintly, almost. He's holding what looks to be a real skull aloft in one hand, 'Alas, poor Yorick, I knew him well,' he says.
Alex stares at him, her face blank. 'That's not Funny.'
'I fucking told you she wouldn't like it,' Leo says. He's in the back. Alex hadn’t even noticed he was there until he spoke. She turns around in her chair, and all she can see of him are two stretched-out legs and his gorilla-hands holding up The Financial Times.
'You normally love this kind of stuff,' Nicholas says.
'I know. I'm in the middle of an existential nightmare.'
Nicholas puts the skull down on the desk. It makes the right noise, like the way Alex might imagine bone on wood to sound. It looks right too: Tobacco coloured, not milky-white like the skeleton they had in her science class at school, and the teeth weren't all even, like you'd expect if it were fake.
Nicholas says, 'Some dead actor donated it to my wife's theater company so that they can use it in productions of Hamlet, and he'd still get to be a part of it. Can you believe that? I wonder if they waited until he decomposed...or if they peeled all the skin off, plucked out his eyes, and scooped his brains out.'
'Who do you want rid of?' Alex says.
'That's what hurts. He's one of our own. He's been running our bar down on Union Street for years. Our accountant noticed discrepancies with the books. Turns out the guy's been skimming off us since day one. I would've roughed him up, but our man here wants him dead.'
'I would've walked in there and shot him myself, if I'd had my way,' Leo says.
'Well, you can't. Alex is going to make him disappear.' Nicholas makes a gesture, like an old-time magician, puff!