Although a sympathetic antagonist can have you on the edge of your seat, sometimes you just want a villain who’s just power hungry and fun to watch. The best way to do this is to have a villain that’s pure evil. These villains are easier to write, often charismatic, and can provide your story with plenty of memorable, quotable lines that your audience will love.
Something you have to make sure they have is a purely selfish motivation. Money for the sake of power, world domination, power, revenge. Maybe they’re just doing what they’re doing just for fun. They’re the opposite of a sympathetic antagonist. A nuanced or sympathetic backstory will make you feel empathy for these guys, which when it comes to a purely evil villain, is something you don’t want. With these villains, you have to love seeing whoever your hero takes them down a peg, or maybe even several pegs.
One of the big keys to making an evil villain fun to watch is a whole bunch of self-confidence, and have them go all out. It's okay to have the villain even be self-aware of the fact that they’re evil. If someone like the Joker from Batman was just standing there, boringly explaining his plan with no humor, he wouldn’t be nearly as beloved. So what the writers did was make him super enthusiastic and into everything he does passionately. His creepy in your face attitude, over the top laugh make him oddly charismatic. Emperor Palpatine from Star Wars is another one. When he’s pacing back and forth explaining his plan, he is bored. But, when he’s crackling, laughing and his actor is putting his heart and soul into putting in an enthusiastic over top performance, he’s really fun to watch.
It is possible to have a purely evil villain who’s more subdued, but it's probably best that you don’t have them be the ‘primary’ or main villain for the first part of the story. One strategy that works is to have your pure evil villain be a schemer who’s managed to recruit a bunch of others to help them in their plans. Show them giving orders to the others, but in order to let them keep the brilliant tactician title, it's best to have them be really composed. A villain who’s all over the top and kind of crazy is scary on the front lines, but seeing a villain who’s able to remain calm and composed, even when the good guys start winning can show that they have something up their sleeve. That’s the reason extremes are generally very good when you are talking about a purely evil villain. Being unable to commit to something completely crazy or completely composed leaves you with something that’s a lot more forgettable, and will likely be unsatisfying to watch for much of your audience.
Lastly, a purely evil villain doesn’t hesitate when doing something bad for morale purposes. A sympathetic antagonist might have at least a moment of pause, or a scene dedicated to them not committing an evil act, but a purely evil villain won’t.