A villain doesn't "need" anything, except to oppose your protagonist.
Your protagonist is a villain in their story, after all.
If you want a sympathetic villain, then write them as you would a protagonist, with agreeable morals and a story that makes sense, but a convincing villain doesn't need that at all.
A villain with a sad backstory (eg: my cousin killed my village and I'm sad so I'm gonna be edgy and blow up the world) is less convincing then say a being that was created to show humanity a mirror of their negativity, and therefore it's in it's nature to harm.
Both ways can be done well and poorly, but it's just up to your writing. In my opinion, a good sympathetic villain example is one who could be a "twist villain", but even after the reveal they're the same character (I know, how could people mess this one up?). They still have good morals and generally do things for the sake of good, but they are in your hero's way. This character can be a complete asshole, (maybe not genocidal maniac unless you're an AMAZING writer) and the audience will probably be able to sympathize with them.
There are no clear rules to this, so just write what you want, and don't think that you have to put the archetype of 'villain' in boxes. And, I guess think about how you want your audience to feel in response to them. That's important too.