His powers could become more nature - oriented. For example, he might be able to control animals better, like Artemis can.
If Percy Jackson was trained by Artemis in fanfiction, his powers could be enhanced in several ways. His connection to water could potentially be combined with Artemis' influence over nature. So he could perhaps create water - based illusions that are more in tune with the forest, like making a stream look like a solid path to mislead enemies. His speed and agility might also improve as he learns the hunters' ways of moving quickly and quietly through the woods.
Well, Percy's powers would likely change quite a bit. Since Artemis is the goddess of the hunt, Percy could gain an affinity for tracking. His ability to sense danger could be sharpened, not just in the water but also on land. His power over water might take on new forms, such as being able to freeze water in the shape of hunting tools like arrows or spears. His relationship with his sword, Riptide, could also be affected. Maybe he would learn to use it in more creative ways, like the hunters use their bows, with more finesse and stealth, rather than just brute force as he sometimes does.
His powers could become more focused. Kratos might teach him to use his water powers in a more precise way, like creating sharp water blades instead of just large waves.
He'd become more powerful. His combat skills would be enhanced, and he'd have a better understanding of the primordial forces. He might also become more unpredictable in battle, like Chaos itself.
If adopted by Artemis, Percy's powers would evolve in a more nature - oriented way. He might be able to communicate with water - dwelling creatures in the wild better. His hydrokinesis could be influenced by the moon, since Artemis has a connection to the moon. So at night, his water - based powers could be stronger. He would also develop a sense of tracking and hunting skills that would enhance his overall power set.
His powers might be enhanced by Stark technology. For example, his ability to control water could be used in more precise ways with the help of Stark - made gadgets.
Well, it could be a really cool story. Maybe Percy would learn some unique hunting skills from Artemis. He might also gain a new perspective on nature and the wild. And perhaps he would have to adapt to Artemis' strict code of conduct.
Percy's relationship with the male demigods would change significantly. Some might see him as a traitor for joining the Hunters. However, he would also gain new allies among the Hunters themselves. His relationship with Artemis would be that of a mentee and mentor at first, but as time goes on, it could develop into a more family - like bond. And his relationship with the gods would be different too, as he's now under Artemis's protection, which might make some gods view him in a new light.
His powers might become more related to fate - manipulation. He could, for instance, foresee certain events related to the destinies of people or creatures. This would give him an edge in battles as he could anticipate the moves of his enemies based on their fated paths.
His powers might become more refined. For instance, his control over water could be enhanced in terms of precision. Instead of just creating large waves, he could manipulate water at a microscopic level, like using it to disarm an enemy by getting into the mechanisms of their weapons. Athena's training could also give him the ability to combine his water powers with strategic thinking. So he could use water to create diversions or traps in a more intelligent way.
His power over water could also be used in a more spiritual way. He could communicate with the water spirits and ask them for help in healing Artemis. The water spirits might then infuse the water Percy uses with their own magic, making it more potent for healing. Percy could then use this enchanted water to heal Artemis' internal injuries as well as external ones.
Naruto's ability to transform, like his Nine - Tails form, could provide a physical advantage in combat. Percy could use his water powers to cool down Naruto if the transformation makes him overheat or to create a protective shield around him. The Son of Artemis might be able to use his tracking skills, which are enhanced by his divine heritage, to find enemies that Naruto and Percy might not be able to sense. His arrows could also be used to disrupt the chakra flow of enemies, while Percy's water attacks could short - circuit any electrical - based ninjutsu, and Naruto's ninjutsu could provide distractions for Percy and the Son of Artemis to attack.