Joker detonates a nuclear bomb at the heart of Metropolis. The clown revels in his success, killing not only Lois Lane, but Superman's unborn son. Batman attempts to calm the superhero, but it fails--Superman kills the Joker by punching through his chest.
After that introduction, the story jumps to before Joker could detonate the bomb. Batman is the focus of the game's first chapter, which has him starting his investigation of Joker's escape. After a fight with Deathstroke, the story continues into space, where Batman must fight Lex Luthor. Taking a page from Mortal Kombat, once Batman's chapter ends, the story will go on to another character, revealing more on why these characters are duking it out.
It's not surprising that Superman has gone evil. What is more surprising, however, is the characters that appear to have turned "good" in an effort to take down Superman and his Superfriends' totalitarian regime.