Past
At some unknown time she became a Shichibukai to make a treaty with the World Government, that would keep her island safe, since they considered all on the island for pirates. She and her sisters had also presumably killed a Gorgon and all three were cursed with eyes on their back that were said to petrify anyone who looked.
[edit] Straw Hat Separation Arc
Hancock's first appearance is three days after Bartholomew Kuma had sent Monkey D. Luffy flying on her island (not to her knowledge). After sailing with her all-female crew, they met upon a Marine ship led by Vice Admiral Momonga, who told Hancock that the Shichibukai were being summoned to prepare for the upcoming war against Whitebeard, due to the execution of Portgas D. Ace a week from then. However, Hancock refused, stating that she would not obey the World Government, even though she fancied her Shichibukai position. When Momonga threatened to revoke Hancock's position if she didn't comply to the summoning, she came up with a make-believe story: The Marine crew would have turned into stone mysteriously.
She also demanded all the treasure on Momonga's ship (which the Marine rookies happily and absent-mindedly complied to), and justified her selfish actions by claiming herself to be "beautiful", which everyone present (save for Momonga) vehemently agreed with. Then, she preformed a special move that mysteriously turned the Marines to stone, save for Momonga, who had stabbed his own hand to avoid the effects of her attack. As her crew sailed away, Momonga remarked that he would wait for two days, and if she didn't follow him, the treaty with the Kuja would be null and void. She arrogantly told him to "Do as [he] pleased".
Upon returning to Amazon Lily, Hancock was greeted with plesantries though concerned that the warriors were not around, due to them chasing after a "monkey". She speaks with Elder Nyon (herself a former Kuja leader) about the danger that would befall Amazon Lily if she does not comply with the Government orders, but she remains arrogant and confident that both her power and beauty will allow her to get her way, throwing Nyon out of a window to prove she was right. When deciding to take a bath in privacy, she unexpectedly encounters Luffy, who falls down into her private area while looking for the person in charge, wanting to borrow a boat. He manages to see the symbols on her back and comments that he has seen them before. She attempted to petrify Luffy, but Luffy, being simple-minded, mistook the beam for a Noro Noro Beam (which Foxy used to slow Luffy down several times) and panicked. The beam did not have any effect on him though. Luffy attempted to run away, but ended up captured and thrown in the arena.
In the combat area, Hancock shows no mercy to Luffy or anyone who tries to defend him, turning Marguerite, Sweet Pea and Aphelandra to stone for attempting to defend him after they admitted to bringing him to their country. At first she attempted to have Bacura execute Luffy, but he knocks it out with a single punch, and after she realizes that Luffy is not attracted to her in any way, and is in fact disgusted by her behavior, she collapses and, out of desperation, sends her younger sisters to attack him in the arena ordering them to bring back his head.