A very good villain does something for a reason. Horrible things - mostly related to snuffing out another human's (or whatever species, point is, living things) life. But, the most horrible feeling that a reader can have is sympathy for evil.
Okay, let's clarify - there are three primary emotions you can feel for "evil" - Horror, Disgust, and Awe.
Horror evil is found in Stephen King's books. Like, the eponymous 'It' from It. It keeps on killing people - nothing much else. It is a thing that most adults can't grasp, only visible to some children. It is tugging at primal ancient fear of children - who find monsters under beds. Is it a hatable villain? Oh certainly, but it is also a villain to be very, very afraid of. You hate its coming on to the page.
Disgust is like Thanos. He has done an awful thing, but can you feel sympathy for his cause? Sure. And that disgusts the audience and tells them that even their morals can be bent. Or Voldemort as to what he does in Harry Potter. He keeps killing, and hates people, and is a not so subtle reference to the Nazis.
The last one is Awe, but that's the sort of "evil" without knowing what it does is evil - the Lovecraftian Horror. The Dark One, from the Wheel of Time, the Joker from Batman all fall in this (the Joker is fundamentally a twisted individual whose plans create horror, but also dazzle you with what he will do. You cannot help but feel awe at him). Feeling awe at something doing fundamentally evil things again creates this tension within the reader.
So this is what makes, to me, a compelling villain in a story.
When it comes to completely hateable and hateful characters, you could select any of the archetypes. Such villains no longer sound compelling, but as a villainess who is a protag, you probably want something more compelling than completely irredeemable.
Also, fiction is very forgiving. Is killing Children irredeemable? Well, SPOILERS, but Anakin Skywalker goes to Jedi Heaven in Episode VI. So, I dunno. What do you find irredeemable?