Villain Complex is a complex of those who wish for recognition for doing villainous acts and/or believe they should ruin other people in some manner.
Some traits of a Villain Complex is:
Bystander Mentality - This can appear as willfully watching other people get hurt (physically, emotionally, financially, etc) in some manner, especially by something of your own creation.
Attraction to dangerous opportunities - This is especially true when those dangerous opportunities involve other people that may potentially be hurt in some manner (physically, emotionally, verbally, etc).
Self-fulfillment in aggression and/or violence - This can appear in a sense of elatedness, heightened self-esteem, enjoyment and/or similar emotions in relation to being the perpetrator of aggression and/or violence.
Purposefully creating a bad image of oneself - This can be as telling (and bragging) to others about something bad you did, say something morally wrong for shock value, purposefully pushing boundaries and/or breaking expectations/notions, etc
Thinking everything one does is inherently bad - This might not necessarily matter on the subject of what the thing in the situation is, though necessarily depends on if one feels if they've wronged someone with it.
Grandiosity - Believing one is greater than others due to the fact of being Villainous, Antagonistic and/or similar terms.
Just a post to describe what a Villain Complex is and the symptoms is because... yeah. (<- No formal thing existing to describe it [Which I wouldn't consider this formal, but I am the experiencer])
Tagging - @radiomogai because might be helpful