My tip is that even crazy characters have like their internal logic. It may be divorced from what is considered normal or healthy, but for them their view just makes a lot of sense. Remember that these characters are still human, they have motivations, dreams, things they like and dislike. The way they achieve their goals or their goals however are probably morally questionable.
One example is like the real life story of a nurse killing her patients. In her eyes she was relieving her terminally ill patients from their suffering and she was fully convinced that she was doing God's work. Jeffrey Dahmer thought that pouring bleach in his victim's brain is a great idea.
It depends how grounded you want the story to be; but I suggest looking at real life examples of serial killers, watch their interviews, watch interviews of victims that have made it out alive, these kinda things. See how they tick and how they talk. Most of them don't talk like the joker lol.
Also, if you want this person to have a mental illness, try to look up some diagnostic criteria, it may help you a bit to make the portrayal a bit more authentic.