We don’t know much of where Aqua’s world or where she comes from. There are a lot of possibilities in regards to this, and it’s unsure if we’re ever going to see it specifically. My headcanon says it’s a lush world where magic is relatively common.
Yet something must have happened for Aqua to become the person she is today - she’s purposeful, driven and steady in her duties of vanquishing darkness and protecting others from it. A part of this is definitely Master Eraqus’ teachings, but I also think she has seen firsthand what darkness can do to a world. As she has all but stamped out the darkness in her own heart, I think it’s safe to assume the darkness that plagued her world come from a group of people within it. This probably happened when she was very young-a year or two after Master Eraqus took on Terra as an apprentice. Since Aqua is probably a year or two younger than Terra, they probably got picked up around the same time of their lives.
Realizing the darkness was spreading and becoming dangerous, Master Eraqus made his way to her world to do his keyblading thing. By this time, however, the destruction was probably pretty extensive - leaving Aqua with few, if any, friends and family. I think Master Eraqus probably rescued the little girl from an encroaching threat, and took some time to make sure she was alright. She probably didn’t say much, but was very appreciative of this brave rescuer. She followed him, despite Eraqus telling her not to, and probably used her magic barrier to protect him from an attack or two (before passing out, because… child).
When the threat was eliminated, Master Eraqus was left with the decision of what to do with this girl. Recognizing her dedication to protect him (or others), and because he had recently taken up Terra as an apprentice, he decided to bring her to the Land of Departure. There she learned to recognize her power with the force light and how she could use her skills to protect other people. She developed and mastered her carefully crafted magic skills, in contrast to Terra’s direct, raw-strength approach. The friendly rivalry between them was probably inevitable.
Aqua also found a family with Master Eraqus, Terra and later Ven. Master Eraqus was her mentor and model for who she strives to be. I’m also fairly sure she also found her voice talking to and arguing with Terra as she grew older (sorry Terra :D;), and looked after Ven as a fragile younger brother that needed to be protected. To her, these three are the closest thing she has to her family and are the dearest people to her heart. She is now committed to her duty as a Keyblade Master, recognizing herself as a guardian of others and her family, like Master Eraqus once was for her. Because of this, it is hard for her to accept protection from others and is especially stern towards those who feel that is necessary because she’s a woman. Really, she came a long way from where she first started.