Batwoman's History
Kate Kane is Batwoman, one of many vigilantes who protect Gotham City using the imagery of a Bat. She is both Jewish and an out Lesbian, playing a socialite during the day, and working with her cousin Bette as vigilantes by night.
Origin
Kate Kane and her twin sister Beth were born to prominent colonel Jake Kane and his wife Gabrielle, herself a captain. Both parents were on active military duty, and worked extensively with intelligence organizations. As her parent were promoted they moved to and from a wide variety of towns and bases, though Jake was often away from home.
Eventually, the Kanes moved to Brussels in Belgium, where they worked with NATO. However, one day, when Gabi decided to take the girls out for the day, they were attacked and kidnapped by terrorists. Though military intelligence managed to locate the hostages, Jacob only managed to rescue Kate, as both Gabi and Beth had been killed. He had tried to prevent her from seeing the worst of it, but Kate was traumatized by the sight of her mother and sister's corpses.
Jacob was a supportive father, and Kate managed to deal with her grief by trying to emulate his cool-headedness. She excelled in school, and eventually got in to West Point academy as a cadet. There, she met a woman named Sophie Moore, and began a relationship with her. When the relationship was discovered, however, Kate chose to come out as a lesbian in order to protect Sophie and was expelled under Don't-Ask-Don't-Tell.
After that time, she medicated her depression with alcohol and promiscuity. Eventually, though, she came across a mugging in progress and tried to stop it. She encountered the Batman, and realized that she felt alive when she was fighting crime. Her father discovered this habit, though, and when she begged him to train her, he agreed.
Kate spent the next three years undergoing fierce training regimens, and exposing herself to the worst that the world had to offer, all in the hopes of preparing her for her destiny. At the end of the third year, Jake gave her one last mission, in which a family had been kidnapped by Russian terrorists, and she would have to rescue them alone. When she found the family, they had already been murdered, and in rage, she nearly killed the terrorist leader. However, she relented at the last second, and the leader revealed himself as her father. The whole thing had been a fakeout; a test to prove that she could stop herself from crossing the line. After that, she was ready to become Batwoman
Elegy
Kate eventually stumbled onto an organization in Gotham City called the Religion of Crime, led by Whisper A'Daire. They believed a prophecy in the Crime Bible, which suggested Kate Kane was the twice-named daughter of Cain, who would need to be sacrificed in order to bury Gotham in flames. Batwoman thwarted these plans, with the help of a defector named Kyle Abbott, and Whisper was deposed.
However, the thirteen covens of the Religion of Crime were revived by a new leader named Alice, whose propensity for quoting Alice in Wonderland belied a sinister and callous disregard for human life, and a persistent obsession with Batwoman herself. In an attempt to get answers, Kate dangled the woman over the edge of a rooftop, but her aversion to killing was known to Alice, and rather than give up answers, she spat a poisoned razor-blade into Kate's face, causing hallucinations.
She was saved by Kyle Abbott and a new sect of the Religion of Crime, who rejected the assumption that Batwoman was central to their doctrine. After recovering, rather than immediately seek revenge, Kate went to a charity ball for the Gotham City Police Department, where she met and began a relationship with Margaret Sawyer. They were interrupted by Kyle, who revealed in private that Alice intended to destroy Gotham by stealing military grade firepower. Given that her father had had to leave the party in order to investigate an emergency on base, Kate realized too late that the Religion of Crime was behind it. Alice had captured her father.
With Kyle's help, Batwoman managed to board the plane from which Alice planned to unleash a toxic gas onto the city. In the fight that ensued, Alice was nearly knocked out of the plane, but Kate caught her in her hand. In a moment of uncharacteristic coherence, Alice looked up at Kate and stated "You have our father's eyes," before plunging a dagger into Kate's arm. In pain, Kate let go, and watched Alice fall to her death as the realization dawned on her that her twin sister Beth had not died, those years ago. As soon as she had regained her sister, she had lost her - and her father Jacob had betrayed her.
Hydrology
When a series of kidnappings and drownings in Gotham's Latino community pointed to the urban legend of a ghost called the Weeping Woman, both Batwoman and Detective Maggie Sawyer began investigating the case separately. While Maggie learned of the origins of the ghost and dealt with the pressures grieving parents, Kate faced with the pressure of reluctantly training her cousin Bette and dodging her questions about her deteriorating relationship with her father. After eavesdropping on one of Maggie's meetings, Kate learned of the location of the latest crime scene. Upon arriving, though, she was accosted by Batman, who offered her a position in Batman, Inc., which she declined.
All the while, the DEO had sent Agent Cameron Chase to determine Batwoman's identity, and through her, learn Batman's. She suspected Maggie, initially, but when Maggie caught Batwoman stealing files from her office, she gave her location up to Chase. From the files, Kate sourced the legend of the Weeping Woman to a boathouse, where she was dragged under water by the apparently real spirit. She managed to escape both the spirit and Chase, but the experience led her to decide to stop training Bette, prompting her cousin to go it alone, where Chase was then free to question her. Before Chase could get to her, though, Bette was attacked by a meta with a hook for a hand, who tore open her gut.
Unaware, Batwoman learned that the Weeping Woman had been an alcoholic mother named Maria Salvaje, whose children drowned at the boathouse due to her neglect, and she later drowned herself as a result of the guilt. Chase, meanwhile, used Bette's desperate condition to trick her into revealing Kate as her next of kin. Returning to the boathouse, Batwoman set the boathouse on fire, to counter the ghost's water magic. As she began to evaporate, Maria revealed that she had been manipulated into becoming a kidnapper by something or someone called Medusa.
Upon her return home, Kate found Chase and Director Bones waiting for her with a deal that they would show her to Bette's location if she would agree to help them take down Medusa. Despite a warning from Batman, Kate agreed, promising herself and the parents of the missing children that she would find them.