He'd likely become more confident. Since he already knows what he's capable of, he can show it right away. For instance, in his first encounter with a monster, he won't be as scared and will be more assertive in using his powers.
His relationships would evolve differently. He would be more understanding of his friends' situations from the start. Say, with Grover, he could support Grover's search for Pan in a more strategic way, having learned from their previous experiences. Also, with the new - found knowledge, he might be more diplomatic in dealing with the other demigods and avoid some of the rivalries that occurred before.
Percy's view of the gods would change. Having lived through all the chaos and manipulation by the gods once, he might be more critical or even try to change the power dynamics. He could start by challenging the gods' decisions more often and advocating for the rights of the demigods in a bolder way. He may also try to bring about more unity among the demigods against any unjust treatment from the gods.
If Percy relives his life, he could completely rewrite the prophecy. He may not make the same mistakes that led him to fulfill the prophecy in the original way. Instead, he could find new ways to deal with the threats to the demigod world, like finding alternative solutions to the problems caused by the Titans and the Giants. He could also have a chance to explore more about his mother's side of the family, which was not much delved into in the original story.
His character could develop in terms of his understanding of the divine world. Since he's with a goddess, he'd get a closer look at how the gods operate, their politics, and their values. This would make him more aware of his place in the grand scheme of things, not just as a demigod but as someone with a connection to a powerful goddess. He might also become more diplomatic as he tries to navigate the complex relationships within the divine realm.
Percy's character would likely become more hardened. Living in Tartarus, he'd face constant danger and that would make him more cautious and strategic. His sense of survival would be enhanced.
His character could become more in tune with nature. The Hunt has a strong connection to nature, and Percy would likely pick up on that. He might also become more self - reliant as the Hunt often operates independently. His loyalty would be tested as he has to balance his old ties with Camp Half - Blood and his new life in the Hunt.
Percy's character would evolve into a more solitary figure. As Chaos, he'd be in a realm where few can understand him. He might struggle with loneliness, yet at the same time, he'd be filled with a sense of purpose that is much grander than his previous quests. His loyalty would shift from his friends on Earth to the well - being of the entire universe.
If Percy were a speedster in fanfiction, his confidence would likely grow. He'd be able to get out of tough situations more easily, which would make him bolder in his actions.
On the other hand, Percy could become more of a revolutionary figure. His act of killing Zeus could inspire other demigods to stand up against the unjust ways of the gods, and Percy would have to step into a leadership role, which would force him to grow in terms of strategy and diplomacy.
Percy's development would be centered around survival and power. In Tartarus, it's all about being strong enough to endure. So he would be more focused on getting stronger. He might also be more isolated, as not many would understand his Tartarus - born nature. His relationships would be more difficult to form and maintain. He would have to learn to control his powers, which might be more closely related to the dark forces of Tartarus, without being consumed by them.
Percy's view of the mortal world would expand. Being in the army, he'd see a different side of mortals - their teamwork, their sense of duty. He might also learn new skills like military strategy that could enhance his demigod fighting abilities. His loyalty might be tested as he has to balance his loyalty to his demigod friends and his new military comrades. And his sense of self - worth could change as he discovers new ways to contribute in a military setting.
His character would become more confident in his artistic abilities. Apollo is the god of many arts, so Percy would likely be exposed to music, poetry, and painting. He might be more flamboyant in his actions and speech, as Apollo has a certain charm. For example, he could start using more flowery language when talking to his friends or enemies.