Hamilton was a barber in the late 1800's. According to Doc Holliday, everyone would go to him to confess their sins. A cattle rancher confessed to Hamilton his sins, so Wyatt Earp tried to use him as a witness in court, but Hamilton never showed up. It turns out that Doc was paid to kill Hamilton, so he chained concrete to his feet and threw him in Big Deep Lake.
Once he was resurrected as a revenant, Hamilton became part of The Seven. Hamilton's M.O. is that he would haunt people and demand that they seek forgiveness from those they've wronged. If they weren't forgiven within the time frame, Hamilton would slit their throat with his straight razor. In The Blade, Hamilton ends up targeting Wynonna Earp. Since Wynonna pissed off a lot of people in her youth, she nearly runs out of time, but with the help of Waverly Earp and Doc, she is able to find where Hamilton is hiding and shoots him with Peacemaker.
As a revenant, Hamilton has gained the ability to move through reflective surfaces. He could even create a three-dimensional “reflection” of himself to act as a decoy against Wynonna When he emerges, he is somehow able to paralyze his victims and kill them by cutting their throats with his straight razor. This paralysis however seemed tied to his challenge to his targets to seek forgiveness; after Waverly forgave Wynonna, Hamilton lost control of her and was easily defeated.