One possibility is that Percy trains his powers with the help of his friends. They could create special scenarios or obstacles for him to overcome, which in turn helps him to develop his powers further. His powers could also start to evolve in unexpected ways during this training process.
Maybe there are some dark forces at work. They sense Percy's growing power and want to stop him before he becomes too strong. These could be ancient evils that have been awakened by Percy's power development. They could send minions or create illusions to make Percy's training difficult.
It could be that Kronos believes Percy has some hidden potential that, when combined with his powers, would lead to a situation beneficial for Kronos. For example, Percy's strong connection to the sea could be used in a way that disrupts Poseidon's domain and the balance among the gods. Kronos, being the Titan of time and a master of long - term planning, might foresee a complex chain of events that would unfold if Percy had his powers.
Obviously Percy himself is the main character. There could also be his friends like Annabeth. She might be supporting him in his training, or even training with him. Grover could also be involved, perhaps using his nature - related powers to help Percy in some unique training exercises.
Well, one interesting aspect could be how Percy overcomes his physical limitations. Maybe he discovers new training techniques that are unique to the fanfiction world. Another aspect could be the relationships he forms during his training journey. For example, he might meet a new mentor who helps him in ways his old friends couldn't.
Well, in most fanfictions where Percy trains in Tartarus, it often involves him facing extreme challenges. He might be learning to control new powers or just surviving the harsh environment. For example, he could be training to fight stronger monsters that lurk in Tartarus.
He might lose control of his abilities. For example, if his power is related to water, he could cause unexpected floods that harm innocent people or damage the surrounding environment.
One consequence could be Percy becoming an outcast among his fellow demigods. Since his powers now come from Kronos, they might see him as a threat or a corrupted being.
Percy's powers as Aphrodite's son would be very distinct from his Poseidon - given powers. He could possess the power of persuasion in matters of the heart. For example, he could convince two feuding parties to make peace by appealing to their love for something or someone. He might also have the power to make love last longer or end more gracefully. His powers would not be about brute force but rather about the subtler forces of human emotion and attraction.
His water - related powers could take on a more primal and destructive form. Since Titans are associated with great power, his control over water might become more like the force of a tsunami rather than just simple manipulation.