Here’s what I’d do. I’d start thinking about her obsession with revenge. Where does that come from? I’d take insanity off the table. (The empathy for someone who is insane is all about caring about those who suffer from illness.) If it’s sadism (which might be seen as a craving), it’s usually followed by unbearable guilt. A sense of letting others down and hopelessness.
If you know people you care about who have disappointed themselves by going back to cigarettes or heavy drinking, that’s a key to empathy. Or it could have its roots in a childhood that was both privileged and chaotic. When privilege becomes a substitute for order, the villain is simply trying to make the world “fair and tidy.” The hurting caused is a side effect (perhaps sad, perhaps unfortunate).
Finding empathy is about imagining explanations, even seeing yourself in their shoes.
However, you may have spent so much time with this character that any excuses are easily dismissed. Even unimaginable. (If you are similarly stuck with your protagonist, you may no longer be able to provide a truly bad flaw. If that’s true, that story will not get a strong character arc. Then you need a less developed, less locked in story to learn the lessons.)
If your villain is frozen, identify a villain you dislike in someone else’s story. As long as it’s not too familiar, you’ll probably find the freedom to develop empathy for that villain. And that could open some storytelling doors for you.