Talia al Ghul was the daughter of Ra's al Ghul.
Talia was the daughter of Ra's al Ghul and one of his most loyal members of the Society of Shadows. Her mother's name, the details of her early life, training, or education were never disclosed. She was first seen acting as her father's agent/emissary. He assigned her to hunt down a former associate of his named Vertigo, who went rogue. During that assignment, she encountered Batman and the two began an on again off again romance and would continued to cross paths several more times over the years. Together, they stopped Vertigo's plan.
Some time later, Ra's al Ghul appeared to Batman in the Batcave and informed him that his daughter was kidnapped along with Robin. That proved later to be a ruse, so that Talia could meet Batman and hopefully marry him, which he refused. After stopping Ra's' plot to "cleanse" the world, Talia prevented Batman and Robin from arresting her father and informed her beloved that they would meet again.
Talia met Batman yet again in order to find her father. That time, however, Bruce Wayne appeared more infatuated with Talia, and even went so far to admit that he cared for her. After they rescued Ra's' from his latest plan, Bruce and Talia parted ways yet again.
Battle with Superman
While she tried to save the life of her father, Talia and some henchmen robbed a train that was holding Native American artifacts. Superman tried to stop her, but in the nick of time, Talia found the Shaman's Staff and used it to subdue him. Combining the staff with a computer, Talia transfered Superman's powers to revive a dying Ra's al Ghul. Though their latest quest was successful, the two were tossed into an underground river after the ensuing scuffle with the Man of Steel and the Dark Knight.
Near-Apocalypse of '09
Although not much was known about that event, it was known that Talia had betrayed her father and helped Batman stop Ra's one last time. Around that time, Bruce and Talia dated at least once in Milan.
After the Near-Apocalypse of '09, Talia appeared to be leading a reformed Society of Shadows, and transformed it into a huge charitable corporation which sponsored numerous projects to improve the Earth's environment. Talia was able to keep her young, beautiful appearance by using the Lazarus Pits like the one in her residence in New Cuba. On Bruce's Birthday, she reappeared to him in the Batcave, offered him roasted pheasant, and a chance to regain his youth.
At first, Bruce decided to undergo the Lazarus Pit treatments, and as such, traveled with Talia and Terry McGinnis to her estate in New Cuba. After he underwent the first treatment, Bruce regained the appearance as well as the body of a physically fit and strong man in his early fifties. After he decided that the Lazarus Pit was a cheat, Bruce decided to stop the treatments. When Bruce decided not to undergo any more Lazarus Pit treatments, the Society of Shadows refused to let them go and then an awful secret was revealed. Some time after the Near-Apocalypse of '09, Talia was purged from her body to house the spirit of her father. Talia's body was destroyed after Terry rescued Bruce and an exposed wire came into contact with the Lazarus Pit, which caused an explosion. After the explosion, Terry wanted to go back in and rescue her, but Bruce stopped him because: "Whatever was in there, died years ago."
Powers and Abilities
Talia was an Olympic-level athlete, and was trained since birth in many forms of martial arts. She was also quite proficient with most hand weapons. Often underestimated, but never quite forgotten, Talia was also an excellent hand-to-hand combatant.
Talia al Ghul was one of several children that Ra's al Ghul sired in his multicenturial existence, and the one that he regarded as the most competent. If she was like her comic counterpart; then Talia served as her father's second-in-command. While Ra's genuinely loved Talia, he was also an avowed sexist, and deemed women inferior to men: thus her husband, not her, was to succeed Ra's. Although Talia followed her father, she was not a villain like Ra's, nor was she a hero like Batman. Her motivations were based on her love for her father and Bruce Wayne, and sometimes supported one, or sometimes another.
Following the Infinite Crisis, Talia revealed to Bruce Wayne that she had borne him a son, Damian Wayne, who became the Robin to Batman's successor, Dick Grayson, and later served as sidekick to Bruce himself after he returned to the present time. Damian's decision to follow his father rather than his mother fueled Talia's enmity for the Bat Family.