Power Girl's History
Kara Zor-El was the Supergirl of Earth 2 and the cousin to Superman, who was raised by Kal and his wife Lois Lane as if she was their own daughter. In adulthood, she became Power Girl.
Origins
Kara was born on the planet Krypton, where she had a cousin named Kal-El and a friend named Val-Zod. When Krypton exploded, Kara was sent to Earth but when she arrived, her cousin had already grown up to become Superman. Kal and his wife Lois adopted her and eventually Kara became Supergirl, a member of the Wonders of the World and friends with fellow vigilante Robin (Helena Wayne).
The Apokoliptian Invasion
When Supergirl arrived on Earth, Darkseid's invading forces had not yet publicly made their presence known. However, in order to protect her from the invaders and have a sercet weapon in reserves, Kal-El kept Kara hidden on a Micronesian island, raising and training her there. As a further precaution, Kal forbade her from leaving the island, even if it was to help someone. However, teenage rebellion drove Kara to periodically sneak off the island when she knew her cousin would be too busy to notice. Using her super-speed, she was able to perform good deeds without anyone seeing that she was not Superman. It was during one such outing that she would meet her best friend, Helena, Earth 2's Robin.
During another outing, rather than simply helping others, she snuck out solely to test her flirting abilities. Sneaking into a club, she experienced both alcohol and romance when she decided to test herself on a young man at the bar. After leaving, the two hit it off, allowing Kara to experience her first kiss, only for her new crush to reveal that he is the son of a world leader and would be returning to his country soon. Moved by his honesty, Kara contemplated telling him the truth when the World government building exploded. Her date gets Kara to safety, then runs to find his father in the wreckage. Once he is gone, she immediately moved to save the building without being spotted. Though she stabilizes the building, the young man returns to the spot he hid Kara in, unaware she was already clear of the building. Before Kara can reach him, he is crushed to death in the rubble. Kara would later discover the one responsible for the bombing, and attempt to capture her. Her failed attempt led her to meet Wonder Woman and learn that her target was her daughter, Fury.
After the war with Apokolips escalated, Kara began serving publicly as a Wonder of the World. Her efforts helped keep the war at a stalemate. When Batman discovered a way to end the war, Kara was kept out of the mission and ordered to guard the nuclear devices that the world's governments had decided to keep to the very last. Superman, Batman and Wonder Woman were killed, but they managed to destroy Darkseid's towers, disabling the Parademons and saving the Earth. As Supergirl caught up with Robin, and without any time to grieve their lost mentors and family, their attention was caught by a Boom Tube portal with a lone figure appearing within it. The Earth's last two remaining heroes plunged into the portal.
A New World
The portal led them to another universe with many similarities and differences from the one they know. After getting their bearings, Helena used money stolen from Wayne Enterprises to establish new identities to blend in. After disagreeing over their course of action, the two decided to take different approaches to life on a new Earth. Helena went on to use series of fake identities to travel the world and fight crime, constantly moving around with her friend's help. Kara used her powers quietly, gathering rare minerals and metals selling them for profit. Using the money, she gathered the world's best scientists and bought or "borrowed" as much advanced technology as possible to create build a major research and development company. Over the five years she spent on Prime Earth, she became a popular public figure (under the name Karen Starr), and quite wealthy. As Helena took up the new identity of Huntress (Robin was taken), Kara decided to assume the identity of Power Girl during her superheroic exploits
During her stay on this Earth she was involved in a relationship with Michael Holt. Their relationship started when Michael invited her as Karen Starr to a fundraiser for Senator Gonzalez's presidential campaign. However, while they were dating, Karen was secretly stealing Michael's dimensional tunneling technology in hopes of using it to return home.
Forever Evil
During the invasion of the Crime Syndicate Kara was tricked by the Thinker, who was using a hologram Amanda Waller to convince her, Steel, Warrant and Unknown Soldier to form a new Suicide Squad team. The team was assembled to retrieve Omac in the Rocky Mountains. Inside the base they were confronted by the remaining members of the real Suicide Squad who were sent by the real Amanda Waller.
World's End
Kara and Helena eventually found their way back to Earth 2, where she and Helena encountered a fake Superman who leading an army from Apokolips. It was during this encounter that she was reunited with her old childhood friend Val-Zod, who was now going under the name of Superman. While fighting the impostor the truth would be revealed that the fake Superman they were fighting against was clone named Bruutal. When Kara and Helena arrived to the scene. When things were getting settled, a massive earthquake heralded the arrival of a female creature that emanated from the fire pit.
They fought against the self-proclaimed Fury of War until she took control of Lois, Helena and Kara with the intention of killing them while she joined her Fury sisters. However, Lois' robotic body managed to reboot their minds and get free. Deciding to go right into the fire pits, they took a detour to a nearby lab that sent a distress signal. The lab was being attacked by mutated creatures that could potentially contaminate the world, thus he and Kara had to combine their speed and strength to generate the impact force of a neutron bomb, effectively destroying the threat and saving everyone.
Inside the fire pits, the heroes found defective clones of Superman and himself, until he sacrificed himself in order to save them. During this, Helena was kidnapped by DeSaad and transformed into a new fury of Apokolips. Kara didn't stop looking for her. The furies were defeated and Helena returned to normal, with Kara not wanting to leave her side.
The battle won, Kara and Val buried the previous champion of Earth on a peaceful hill before traveling to a World Army outpost. Later, they joined Commander Sato and Steel on Atom's Heaven HQ when Apokolips' terraformer fell to Earth. Kara, Val and Lois begin their attack against the terraformer, forcing it to unleash Parademon hordes to distract them until Commander Sato commanded them to attack Apokolips itself, crossing paths with a weathered Green Lantern who failed to shield Earth from Apokolips.
After managing to save the rest of the people, Val, Flash, Green Lantern and Yolanda Montez were teleported to an unknown planet by a being named Telos, who also kidnapped several other heroes from other universes to fight each other (at the behest of Brainiac). Eventually, Val and the others managed to escape and briefly allied with Deimos, before he revealed himself as a villain and tried to destroy them. During this, Telos regained consciousness and helped them defeat Deimos, but the energy he released would destroy the planet with them all. So with Brainiac's help, they were saved and sent back to a new Earth 2.
A New Society
In the new world, Kara and Val started rebuilding the cities and eventually started dating, but their powers didn't work all the time as the sun on the new planet was different. They broke up after an argument over Clark's death.
Meeting Harley Quinn
Due to an alien attack, Kara was thrown back into Prime Earth, where she lost her memories and fell at the feet of Harley Quinn. Eventually, they became partners and fought crime together before being sent across the universe on a mission to return home. When Kara regained her memories and realized that Harley had lied to her, she was initially angry but forgave her. However, when Harley hit on her, Power Girl left her on top of the Eiffel Tower.
Justice Society of America
When Doctor Manhattan restarted the universe, Kara became a member of the Justice Society of America. During the events of Infinite Frontier, Kara and other JSA members arrived at The Bleed and attacked Roy Harper by assuming he was a zombie from an alternate world in the Omniverse.