Batman is such a captivating hero in large part because of his wide array of terrific villains. For an example of that you can look at Selina Kyle, Catwoman. Her early life was defined by constant tragedies which eventually led to her becoming the iconic character. She is a villain, and a hero in some instances but mostly she looks out for good ol' numero uno. She worked predominately in shades of grey as her moral compass never strayed to much to evil or good. She frequently went by her own moral compass where she abhorred killing, albeit she did eventually kill Black Mask, another villain in the Batman universe. She was sometimes an ally to the Bat when there would be a great threat present on Earth or even just in Gotham. On one occassion, she even went as far as to save the Justice League of America. Due to her lack of a moral compass, Batman always had a hard time understanding her but there was frequently a sort of sexual tension between the two. Catwoman understood him, whereas Bruce Wayne's other flames couldn't due to his inability to come clean about his alter ego.
When Selina Kyle was just a young girl, her parents had early deaths. Her mother was constantly berated throughout her life which led to her committing suicide and her father drank himself to an early grave. After all the unfortunate deaths, her and her younger sister Magdalene were separated as Magdalene went to Sprang Hall Juvenile Detention Center which just so happen to be an abusive state home for orphaned young girls. Selina choose to take her chances on the dangerous streets of Gotham City. She managed to survive on the streets through petty theft, which she developed quite the skill for. She became one of the slickest cat burgulars that the Gotham City Police Department had come into contact with in large part due to her natural skills as a gymnast. She then turned to an ex-boxing champion Ted Grant to teach her how to defend herself in battle which helped her become the most accomplished thief around, yet she was also one of the most generous. Whatever she gained in a score, she would spread out her winnings across the East End of Gotham where the less fortunate lived. One day she crossed paths with Batman as he was fighting other criminals and she felt inspired in a way. She saw how he wore a costume and decided it was time for her to create a dual personality of her own for the moments she was prowling the night.
Upon putting together a costume and naming herself Catwoman, she was initially introduced as a villain of Batman's but her role as a villain or hero has been rather ambiguous over her years. Where as Batman has lived a very black and white lifestyle in making his decisions, Catwoman prefers to stay in a grey area where the line between good and evil often blurs. Batman also develops an attraction to her due to her conflicting personality and because she in a way is a reflection of himself, in female form. The two are both costumed vigilantes roaming the city living by their own moral codes trying to make things better, or in her case, worse. During the events of "The Long Halloween", Selina visits the man that she believes to be the illegitimate daughter of, Carmine Falcone. Falcone was one of the leaders of the local mob in Gotham. However, she was unable to find any substantial proof to prove it and met Mario Falcone, Carmine's son, who would eventually take over as head of the Falcone crime family. During the events of "Crisis of Conscience", Catwoman sought out to prove herself as an ally of Batman's. To do so, she aided Batman and the Justice League of America against the old Secret Society, who she previously had worked for. In the battle, she was wounded and taken to the Batcave to recover. Despero, a frequent villain of the League, brainwashed a few members and infiltrated the cave while also brainwashing Batman. In this time, Catwoman was able to send out a distress signal to the unaffected members and after a fierce battle Despero was subdued. It was all a hollow victory as the mind control brought out pre-existing animosities between the heroes. Batman asked Catwoman about her wounds only to be quickly dismissed as she left saying he had done enough already.
Following the run in with Despero, despite the drama that ensued afterwards, Catwoman seemed to be reformed and in love with Batman. At the start of the "One You Love" storyline, a group of super villains seized control of East End, forcing Selina to join the new incarnation of the Secret Society. With her initial intentions unclear, many assumed she had gone back to her normal self, yet she had shared her plans with Batman to infiltrate and destroy the villains. To start of she made a deal with a criminal who had similar powers to Clayface, and for his help she guaranteed him his freedom. His part of the deal was to impersonate her as the villains opened fire on him thinking he was in deed Selina. He was able to take all of the bullets doing no harm to himself, leading the villains to believe she was dead. With the wide belief that she was dead, she slowly was able to pick off all of the villains one by one. While dealing with the villains, she ended up shooting and killing Black Mask. During the story line, "One Year Later", Selina Kyle is no longer Catwoman and left East End as she is now a mother. Her daughter is named Helena and Holly Robinson takes over as the new Catwoman, but Selina can't stay away from it long despite being a mother. Holly takes the fall and gets arrested for the murder of Black Mask. Selina then breaks into the police station and successfully frees Holly only to come home to find a man named Sam Bradley who deduced that he is the father of Helena. Shortly afterwards, Batman asks her to help him take down a violent tribe of Bana Amazons. The two do so successfully as the tribe had planned to launch a terrorist attack on a massive scale against Gotham. Catwoman then invited herself to become the newest member of Batman's Outsiders group. The two also began to have a romantic relationship, that they frequently hid from others but at times they also had their special moments.