Edward Nashton: Ed is trying to expose some sort of conspiracy that Wayne enterprises is a part of. Edward was probably part of either the GCPD or Wayne enterprises or the mayor’s office and was tired of the corruption of Gotham and became the Riddler to expose the truth. This would start a movement for the Riddler to the point they joined Riddler in his goal. He labels himself as Batman’s secret “friend”, acting like the dark knight’s ally. Batman would eventually realize that Wayne enterprises is a part of this conspiracy, explaining why Riddler told him he’s a part of it. After Riddler is arrested (or killed), Batman makes a vow to defeat the corruption plaguing Gotham, the high and the low.
Oswald Cobblepot: Oz is a gangster who seeks out to take down Carmine Falcone. Oz leads a group of goons (the ones with paint on their faces), who call him “Penguin”, a name he dislikes because in his childhood, he was bullied and given that name as a way to be made fun of. This is why he wants to make a name for himself, and the Riddler’s actions make Falcone’s empire weaker, giving Ozzie the advantage of taking Carmine’s empire for himself. After Falcone is killed (or arrested) and the Riddler is arrested (or killed), Oswald takes over the remains of the Falcone crime family and embraces his nickname: The Penguin, becoming the leader of the new Cobblepot crime family.
Selina Kyle: Selina is an old friend of Bruce’s who works for the Falcone crime family. She has secretive desires to take down Falcone for killing her real parents right in front of her as a kid. She will take the identity of the Cat, or “Catwoman” as the media calls her, to rob whatever is valuable for the Roman. Catwoman, just like Penguin, will use the Riddler’s actions to her advantage and defeat Falcone. She also crosses paths with the dark knight and either assist him or battle him. After Falcone’s death and Riddler’s arrest, she becomes popular in the Gotham underworld and might cross paths with the Penguin.
Carmine Falcone: the Roman of Gotham, Falcone is part of a conspiracy between Gotham’s finest. Carmine used to be the adopted father of Selina and a mentor for Oswald, but both would turn on him eventually. During the final battle between Batman, Riddler, Catwoman, and the Penguin, Falcone joins and attempts to kill the four of them (Batman because he was taking down his business areas, Penguin and Catwoman for their betrayals, and the Riddler because he was trying to expose the conspiracy). When Batman gets defeated (for a few moments), the three kill Falcone with Catwoman stabbing him with her hand claws, Riddler using a crowbar to beat him (or shoot him), and Penguin putting the former Roman out of his misery by shooting him in the head. With Falcone dead, Penguin and Catwoman take his empire and businesses, Penguin transforming the crime family into the new Cobblepot crime family and Catwoman taking Falcone’s values.