The key elements include a complex villain character. They should be intelligent, calculating, and have their own set of values (albeit evil ones). The plot usually revolves around the villain's rise to power or their attempts to achieve a certain malicious goal. There's also often a moral gray area where the reader might even find themselves sympathizing with the villain at times. For example, if the villain was wronged in the past and is now seeking revenge in an extreme way.
A true villain in manhwa is usually someone with a deeply selfish and malevolent nature. They often have no redeeming qualities and are driven by pure evil intentions.
The villain with a crush might show conflicting emotions. They could be cruel in their usual actions but soft and vulnerable when it comes to the person they have a crush on.