Talia al Ghul is the daughter and right-hand of Ra's al Ghul and an occasional enemy of Batman.
She traveled the world with her father and learned numerous skills from him. Talia is also Batman's love interest but her loyalty to her father keeps them from being together. She would occasionaly betray her father and help Batman or vice versa. Talia is an antagonist in the video games and the movie The Dark Knight Rises.
Son of The Demon
Talia and Batman have a passionate, yet strained relationship. Over ten years ago, the two engaged in a sexual relationship that left Talia pregnant (The details surrounding this incident change depending on the story, such as whether or not the two were legally married). Her son, Damian Wayne, would eventually become the fifth Robin.
At some point after the Son of Demon, she bcomes the new CEO of Lexcorp following Lex Luthor's nomination as President of the United States. While apparently working under Lex, she secretly tries overthrow him and eventually sells all of Lexcorp's assets to Wayne Foundation, leaving Luthor broke.
Red Hood-The Lost YearsWhen Jason Todd was killed and subsequently resurrected-albeit with brain damage-Talia took him in, hoping to win Batman's love by taking care of one of his sidekicks. When Talia threw Jason into a lazarus pit, he emerged mentally restored. Talia then told him that his death had gone unavenged and kept a watchful eye over him as he spent the next year travelling and acquiring new skills. Jason may have had some romantic feelings for Talia during this time, as they slept together shortly before he made his debut as the Red Hood.
Batman and Son
After the death of Ra's al Ghul, Talia became an increasingly villainous character, inheriting the League of Assassins and upgrading all her mercenaries using Kirk Langstrom's formula to create an army of ninja Man-Bats. She kidnapped Bruce Wayne, reminding him of the events in Son of The Demon, and introduced him to their son, Damian. This was revealed to be a distraction for the detective, as Talia instigated a terrorist attack whilst Damian ran around Gotham wreaking havoc. Damian showed that he was inherently heroic by siding with his father instead of his mother. Talia would then declare war on both father and son for this...
Talia becomes the head of the sinister terrorist organisation known as Leviathan. She sends moles to infiltrate the infrastructures of various communities, particularly Gotham. These moles then go about indoctrinating children under the guise of teachers and other figures that children are told to trust.
Talia also manages to clone Damian, artificially grow the clone to adult size and use him as a personal bodyguard. Ra's al Ghul tries to reason with Talia, saying that her vendetta against Batman will do more harm than good, but Talia will not listen. Talia then orders for Damian's execution as a way of spiting Batman for turning their son against her.
In other media
The Dark Knight RisesFor more information, see here
Talia al Ghul, under her alias Miranda Tate, is a supporting protagonist turned the hidden main antagonist of the third and final Dark Knight trilogy movie, The Dark Knight Rises. She is the heir and the leader to the League of Shadows, with her friend and partner, Bane, serving as the field commander.
In the movie, she was portrayed by Marion Cotillard and Joey King.
Main article: Talia al Ghul (Arrowverse)
Talia al Ghul appears in the CW-owned shard universe, albeit very briefly. She first appears as a child in 1960 in the DC's Legends of Tomorrow episode "Left Behind", and appears in Season 5 of its parent series Arrow. She is Ra's al Ghul's first child, but went unseen during previous seasons, replaced by Nyssa al Ghul, her younger half-sister.