|“|| Superman: You killed him.|
Zod: I did. And not a day goes by when it doesn't haunt me... but if I had to do it again, I would. I have a duty to my people, and I will not allow anyone to prevent me from carrying it out!
|~ General Zod explaining his amoral motivations to Superman|
Characters who are amoral are unable to be truly judged by our concepts of right and wrong, or happen to lack a moral sense, thereby being unconcerned with notions of right and wrong.
Almost all abstract and godlike entities fall under this category. On a non-cosmic scale, however, an example of an amoral villain would be a mindless machine (that runs on a program), a predatory animal (which is guided by instinct), or an individual who doesn't conform to the traditional archetypes of good or evil (such as Deadpool, who doesn't care what side he's on).
By definition, Complete Monsters can NEVER qualify as they are aware their actions cause others harm and take pleasure in it. They even commit these actions for the reason of causing others harm.