This is actually a really hard question, because I love a lot of villains, but I moreso love them as characters and don't always necessarily love them as villains.
The villain I feel most comfortable going with for my answer at the moment I guess would be Grima from Fire Emblem Awakening. The present story of Awakening is a bit shaky, and most of the characterization you get for Grima is from what you hear of Lucina's future; his backstory is rather nonexistent. But he's ruthless and cunning with a very strong hatred of humanity and Naga, and the apocalpytic nature surrounding him makes him so damn extra and I love it.
Now, my relationship with him as a character is kind of weird, because while I liked his villain role and his ties to Robin, his lack of backstory just makes him like... kinda there. Villains like him are like so sinister for the hell of it, they're not particularly relatable as characters, so it's hard to understand this sort of villain without a backstory. Him being unexplained made a greater disconnect between his savagery and the player. And I always felt conflicted about that, because I really wanted to like him as a character more; he has a really neat design and concept. But in Awakening, he's pretty one dimensional, despite how interesting his cryptic vibes and connection with rituals may be. When I first got the artbook for Awakening, I remember flipping through the pages on him and saying something like, "Man, there's so much potential here than what we got. I wish they did more with him."
Fire Emblem Echoes delivered (that was a bad pun and I'm not sorry) on explaining his backstory and it was done in such a fashion to suit his occult origins, it has completely compensated for the lack of information in Awakening, at least for me. It makes sense why this information wasn't provided in Awakening, all things considered. It's almost a forbidden knowledge that the characters in the game could have not possibly known, and therefore there would not have been a way to give this information to the player without destroying his mystery. His lack of explanation could have probably been dealt with better within Awakening, but despite that, the information given in Echoes builds upon while remaining very consistent to Awakening, to the point that I am very certain Grima was designed with this backstory in mind from the start--and the writers just had no idea how to express this in Awakening. Either way, I love him, and his hatred of Naga is suddenly understandable--as is why he cannot be slain by Falchion--and I really would love to see him appear as a villain again just to get more of this sort of content.
He wasn't a particularly difficult boss in Awakening, but I've never fought him on lunatic where he has broken skills I guess. But you don't fight him directly; you just fight his vessel. But his fight/map in Echoes was sufficiently challenging and I really had to carefully plan my advance. I probably would have struggled more if I didn't have strong archers with me, though. Also, Grima's head does a weird thing at low health in Awakening, and it was just kind of a random cosmetic change that raised a lot of questions at the time. But Echoes also explained that. It's incredible how such a small side story can fill in so much. I love that sort of storytelling. I love piecing things together.
