Self-Aware

Self-Aware villains are often depicted as having "Heightened Awareness", which is popularly known as "breaking the fourth wall" and was very common in the early days of media but became less popular when works tried to suspend belief; however, it is still extremely common in less serious or more surreal works and is also a very common device for certain types of characters.

Often, these characters are seen as insane by those in-universe or exist in such a manner that they are fully aware of being "fictional". Advanced reality-warpers as well as extremely unstable and alien beings are likely to have this trait, depending on the writer and/or setting.

In other universes (usually comedy or cartoon-based), it is very common for characters to break the fourth wall and it is accepted as part of everyday life.

Basically, characters who either know they are "fictional" or can interact with their worlds in ways that are impossible (such as taking text from a title screen (Bill Cipher), interacting with the audience (Glitchtrap), or stealing paint brushes from their animators (Most of the Stick Figures), etc.) without being full-on reality-warpers can be added here.