Love to Hate:
To love to hate a villain, the villain must be clever, must outsmart the protagonist, and must usually (nearly always) win. They must be competent and difficult to defeat.
The audience must fear what the villain does next, not so much in terms of violence but the audience must think the villain will probably succeed at what he does next.
Hate to Love:
You must make your villain something that is not pure evil, but more like mentally disturbed into believing that what she is doing is done not for greed or wealth or even power, but for the good of others.
An anarchist may truly believe, for example, that big government is always and irrevocably and inevitably corrupt, and can show their proof of it, and is therefore the enemy of mankind to be destroyed. Sure, innocent lives are lost as in any war to save mankind: How many women, children and infants were lost in Hiroshima and Nagasaki? In the carpet bombing of Berlin and London?
An aspiring world-dictator might truly believe they know how to run the government for the betterment of the people, to make them happier, more free, and better off. After all, didn't the Founding Fathers of the USA think the same, and succeed, in winning independence from England? Didn't the leaders of the French Revolution do the same? Every happy monarchy in the Netherlands, consistently shown to have the happiest citizens on Earth, began with a conquering King. A dictator!
Many great villains are just greedy, ruthless psychopaths, but they are great villains because they (almost) never make a mistake. They may have setbacks but overcome them. They are hard to beat and the hero fails to beat them, time and again. They stay a step ahead.
For the "Hate to Love" variety, you can love a villain out of sympathy, pity for the undeserved events that broke them and made them who they are, and because they are sincere in their desire to change the world for the better. But the things they do in that pursuit are horrific, intentionally killing innocents, torturing the guilty, literally waging a war in which objectives outweigh any sense of morality and no price is too high for victory.
We can certainly recognize their mindset, with reference to actual wars; In WWII there are 15 million military deaths but 45 million civilian deaths; three times as many and tens of millions of non-combatants killed on both sides.
Did the ends (victory for the Allies in WWII) justify the means (wanton killing of innocent men, women and children born in dictatorial countries)?
Again, most of us believe winning WWII was worth the price, and if we admit that, can understand the villain even if we are repulsed by their brutality.
Now the villain does not require a grand cause like that. To make one up, say my villain is out to assassinate a single corrupt billionaire, a smart psychopathic CEO, for example. My villain's inciting incident is the death of his wife and only daughter, killed by pollution leak. The CEO is responsible, our villain has gone a bit crazy but he is right, and one way or another he is going to get to this well-protected CEO that put his profits above the lives of his wife and daughter and hundreds of others, and will again. No matter how many protectors and enablers he has to kill on the way, if he has to kill innocents he will because this is war and the CEO is the great threat and must be stopped, by stopping him he will save thousands of lives, perhaps millions because his investigations show this CEO is actively bribing politicians to pass legislation that will let him do even more harm.
Our hero? The ethical cop leading the team to try and stop him, but they keep getting outsmarted. (Hey, wait, I'm not even sure who should win.)
Back to the general case: To accomplish this (and it is not necessary for a great villain), your villain must not enjoy the killing of innocents or torturing of his enemy for information. (That kind of angry celebration/relief at a victory is fine, of course.) His goals must be pure and, in his twisted way, non-selfish. The audience can know in their heart he is both a sincere believer and wrong. Or that he aims to right a wrong no matter what the cost.