No, they don't. What a villain needs to be "good" is to be an effective antagonist to the hero - somebody who the hero has to work at, fight, and sacrifice in order to defeat. Outside of that, the normal rules of character development apply (must want something and be using their agency to get it, must take actions that make sense for their character to take, etc.).
That said, "good" and "memorable" are two very different things. A tragic backstory can help, but it's not needed. Hannibal Lecter was one of the most compelling villains in fiction long before Thomas Harris decided to give him a backstory. Emperor Palpatine has no tragic backstory, and he made it into the modern mythology. Sauron has no tragic backstory. To be memorable, there must be something that sets the villain apart from the crowd (Darth Vader's visual design, for example).
And yes, a memorable villain is hard to pull off.