Open the movie with the end of MOS, show Bruce arriving, running into the rubbel, basically the same thing.
OPENING TITLE.
Batman is a reckless, vicious vigilante. He pummels criminals like rapists and murderers into near comas. Alfred is deeply concerned about Bruce's growing viciousness, fearful that he'll cross the line. Have the scene where Alfred says that everything's changed also have him glance at Jason's costume just as he says it. Jason's death caused him to shut down as a superhero, but after the events of MOS, he's retaken his mission harder than ever. He has nightmares about his parents deaths and Jason's death intermingling into the same event.
Superman is very much playing with kid gloves. After the events of MOS, he's afraid of his powers, the destructive force he has. He doesn't break bones, he tries to avoid destroying property. He doesn't want anyone else to get hurt. He has ptsd-esque flashbacks about the events of MOS. He still works, he's begun a relationship with Lois, which is struggling because of his disconnected attitude. Clark is obsessed with keeping himself from being something that frightens people, so much so that he's formed a partnership with Metropolis' hometown billionaire to help the city...
Lex is paranoid, rich, ruthless and fearful. As a former abused child, he's grown and constructed his entire life around being powerful, great and untouchable. And then comes Superman, a powerful creature that is better than him, more special than and more powerful than him, something that he can't control, that he can't protect himself from and he can't stand it. He's basically Batman on steroids. The Bruce Wayne worst case scenario. Only in a more self-involved way. He views Superman as a threat in waiting to him personally, not just really the world. Keep Jesse Eisenberg if you must. But make him more physically fit, not overly muscular though. Maybe he trains in some form or multiple forms of karate. He finds any form of inability as inherent weakness.
Side threats Metallo and Bizarro. When Lex will reveal this to Superman he will say, "Aliens, metahumans, magic, it's truly bizarre times we live in. Only fair that we make something just as bizarre to combat it."
Lex uses the kryptonian ship and a sample of Superman's DNA to create a clone, a mentally deficient clone, even a decaying one, something that he can control. He uses it to frame Superman for attacks. This shakes Superman. He sees the public and understands that no matter what he does, he won't be trust by them. He nearly quits because of this. It's really all about Superman's sense of inferiority. He's afraid that he can't help people now that they know he's out there. He's afraid that even though he knows the attacks happening aren't his fault he still fears that it's something he could be capable of. He doesn't see himself as helpful to the world, but as a negative force in it.
There's a running theme of a feeling of inferiority in this story. Lex feels inferior, because Superman's existence makes him feel powerless and inadequate. Batman feels helpless as ever to do good, to help people, because of such a destructive creature like Superman being around. This feeds into his already intense powerlessness at the loss of Jason Todd at the hands of the Joker due to his, as far as Batman's concerned, inaction.
Batman and Superman cross paths twice before the fight. Once during a bank robbery and another during an altercation where Superman does x-ray through Batman's cowl and tells him to stop his vigilantism. Batman rejects this and begins building his suit to combat Superman after he sees the stories about Superman's attacks that are really Bizarro. Superman does some digging on Bruce Wayne, finding out about his parents deaths and the death of his ward, Jason Todd.
Meanwhile Lex has been keeping tabs on Superman and kidnaps Lois Lane or his mom, framing Batman for it, placing a batarang at the scene.
Superman is basically winning the fight, until he stops himself and begins to realize that he and Batman have been manipulated by Lex. Batman capitalizes on Superman's stopping and uses his kryptonite weapons. And Batman begins beating Superman brutally, mercilessly, and we see flashes before Batman's eyes of Jason Todd being beaten half to death by the Joker with the crowbar. He would tell Superman that he's let too much death happen because he wouldn't do what was necessary and that he won't let that happen again. But Superman would convince Batman that he doesn't have to do this, to cross this line, that he understands how he feels.
They would defeat Bizarro and Metallo together. Maybe Wonder Woman could be involved, but she's not really a real problem in the movie, so i didn't think about her character.
Lex would lose his hair when Bizarro unleashes a hit of fire breath onto him after he's been defeated by Superman, burning his head.
Have a very great day everyone!
God bless everyone!