Jason Todd is probably the most insane member of the Bat Family. Todd, as the second Robin to Bruce Wayne’s Batman, was killed in horrific fashion by the Joker, only to be resurrected as the cold blooded vigilante called the Red Hood.
As the Red Hood, Jason feels that Batman’s refusal to kill is his true Achilles’ heel. Opting to go where Batman won’t, Red Hood uses his mercenary skills to be judge, jury, and executioner in the streets of Gotham.
When Bruce Wayne is thought to be dead after the events of Final Crisis, Jason sees this as an opportunity to pick up the cape and cowl, and do things his way. With no permission at all, Jason shows up in a custom Batsuit, and dual pistols, claiming to be Batman. This does not sit well with Dick Grayson, the first Robin, who isn’t aware that Todd has stolen the mantle.
Appalled by this Batman’s violent crime-fighting methods, which include the murdering of criminals, Grayson faces off with his former ally Jason, winning the ensuing battle and stripping Jason of the mantle. With Todd out of the picture, Grayson adopts the Batman moniker, keeping it safe for Bruce’s return.