I am writing this to add to the multiple theories on how Batman's venture in the current DC Cinematic Universe will go.
During Dawn of Justice
Batman prepares to go to Metropolis to investigate the "alien threat". He contacts Nightwing, who he hasn't spoken to in a while, and Batgirl, and asks them to help Robin (Jason Todd) watch over Gotham in his absence. He and Superman defeat the villain of BvSDoJ, and while they discuss it, Nightwing calls Batman and tells him he needs to get to Gotham immediately. Batman arrives, and finds out that Jason has been killed by Batman's long time enemy, the Joker.
The Batman (First solo movie, after the Justice League) with Hugo Strange as the main antagonist, and Clayface as a secondary villain, with his backstory being slightly explained. Batman and Nightwing still blame themselves for Jason's death, and Bruce constantly looks at pictures of Jason, as a reminder of the one person he couldn't save.
The Shadow of the Bat (Second solo movie) The Joker is the primary villain, and Killer Croc and/or Man-Bat or secondary villains. The Joker taunts Batman, Batgirl, and Nightwing about failing to save Jason. During a fight between the Bat-team and the Joker, the Joker knocks Batman off the roof, knocks Nightwing out, and kidnaps Batgirl. While the Joker has her captive, he shoots and paralyzes her. Batman rescues Batgirl, and she and Nightwing return to the Batcave so she can recover. In the final fight, Batman subdues the Joker, and throws him in Arkham Asylum along with Killer Croc, Man-Bat, Clayface, and Hugo Strange.
Meanwhile, while Batman is turning in the Joker, a mysterious man and woman are seen standing before a pool. Screams of terror and pain are heard coming from the pool, then suddenly, a figure rises from the pool: Jason Todd.
The Dark Knight Falls (Third solo movie) Red Hood is the primary villain, and various villains are the secondary antagonists. Batman is still distraught over the death of Jason Todd and Barbara Gordon's crippling at the hands of the Joker. He goes to investigate when he hears of a mysterious figure roaming Gotham, killing criminals. He confronts the man, known as Red Hood. Batman gets in a fight with Red Hood, and both leave with wounds. Batman returns to the Batcave, and Red Hood decides to strike back against Batman, by releasing the inhabitants of Arkham, and he recognizes one of them as the Joker. While the other criminals wreak havoc on Gotham, Red Hood kidnaps Joker and takes him to an abandoned warehouse, where he beats the Joker with a crowbar, and unmasks, revealing himself as Jason Todd, the boy he killed years earlier.
Meanwhile, Batman deduces Red Hood's identity, as he recognizes his movement, and mannerisms. He heads out to fight the escaped criminals, and drags them all back to Arkham, where he discovers the Joker has escaped as well. One of the psychiatrists, Dr. Harleen Quinzel, tells him the direction Red Hood went with the Joker.
Batman finally gets to the warehouse, where he tells Jason he figured out who he was. Jason angrily curses Batman, for being unable to save him, and asks why he won't just kill the Joker. Batman says he will never kill, because it would make him no better than the Joker. Jason then forces Batman to either shoot him or the Joker, and tosses him a gun. Batman refuses, and walks away, and Jason shoots at him. Batman throws a Batarang at Jason's gun, stopping it. Jason shoots, and hurts his hand, and he falls down. The Joker gets up and tries to run away, but Batman tackles him, and they fall out of a window, only to be caught by Nightwing, who flies by in the Batwing. The Joker is returned to Arkham, and Batman, Nightwing, and Jason go back to the Batcave.
The movie ends with a young boy approaching Batman, asking to be made the new Robin. He shows Batman his fighting skills when a gang attacks Batman and the boy. Batman, impressed, asks the boy's name: Tim Drake.
Thank you for reading, Pilots! And yes, parts of "The Dark Knight Falls" were inspired by "Batman: Under The Red Hood" and I know, parts of these were admittedly pretty lame, but, I beg you, have mercy on me in the comments. No need for a YouTube-like argument. And if you think they would ever go past three movies, and would like for me to write more, let me know. And if you don't, LIE. ;)