Lex gives him an ultimatum and Batman provokes him. He finds a way out of Lex's "kill or be killed" scenario, brings out the good in Batman, and gives his life to save a world that fears him. He proved he was a hero to Lex, Batman, and the world and he didn't need to operate on anyone else's rules. He was finally sure of himself when he told Lois "THIS is my world. YOU'RE my world." He was portrayed as a hero through and through, and much more confident than he was in the previous film. I'm now more sure he's going to be the hero he's grown to be in the comics in the next film.