How to write a villain protaganist that's evil but somehow likable?
This type of story focuses on a villain who has an "interesting" moral compass, one vastly different from the rest of society. Because of this, she views most people beneath her ethically and acts such as robbery, murder, extortion, human trafficking, etc. are perfectly legitimate in her eyes. But we can all agree those are pretty heinous actions, right?
Problem is how to captivate reader attention while she's doing these things, and I'm not exactly sure how to do that.
Answer: Your challenge certainly is to make the reader sympathetic to this character, but it can be done.
One way is to make clear that the protagonist, while not a good person, is better than the people she is doing bad things to. An obvious example: soldiers kill, but their killing is justified when it is clear to everyone that the enemy is worse. Enemies are always de-humanized to avoid moral qualms. This is why the Sheriff of Nottingham is always portrayed as more evil than Robin Hood.
A variation is to give your protagonist a noble cause that justifies their actions, such as caring for an innocent person.
Another approach is to make the character charm the reader. This is particularly effective in first person narration, where the character can treat the reader like a confidant (which is flattering to the reader). An example of this would be A Clockwork Orange. It helps if the protagonist is witty and a good storyteller.
Of course the other technique used in A Clockwork Orange is to give the protagonist some redeeming quality which the reader can sympathize with (Alex's love of Beethoven).
Finally, it helps of you can make your protagonist an underdog, always fighting bigger opponents and never quite winning.