He might be confused at first. Percy has always been a bit of an outsider among the gods, but he may not expect Artemis to hate him. So he would try to figure out what he had done wrong.
One possible reason could be a misunderstanding. Maybe there was some miscommunication or false information spread that made Artemis think Percy had done something unforgivable. For example, if Percy was wrongly accused of harming one of Artemis' beloved creatures or desecrating her sacred places.
It could be that Percy gets involved in a conflict where he sides against Artemis' hunters. His actions in this conflict might make Artemis view him as an enemy. For example, if he accidentally harms one of her hunters while trying to protect someone else, she may grow to hate him.
One possible reason could be a misunderstanding. Maybe Percy accidentally disrupted one of Artemis's hunts or sacred rituals in the fanfic. Another reason might be that some prophecy or fate in the fanfic's made - up world has pitted them against each other. For example, if there's a prophecy that Percy's actions will somehow limit Artemis's power or freedom in the future.
One possible reason could be differences in their divine natures. Percy is a son of Poseidon, a god associated with the sea and a more fluid, emotional element. Artemis is a virgin goddess of the hunt, very strict and unyielding in her ways. This contrast in their essences might lead to clashes and Percy's dislike.
Often, it starts with a small incident that sparks the hatred. For example, Percy might save a person or creature that Artemis was hunting, thinking he was doing the right thing, but from Artemis's perspective, he's interfering. Then, the relationship deteriorates as more misunderstandings pile up. Artemis might start to actively oppose Percy in his quests, using her own powers and influence against him.
In the original series, Percy has no such extreme hatred towards Artemis. So, this fanfiction is a major deviation. In the original, they are more like distant acquaintances with different roles to play. Here, the hatred creates a completely new dynamic that changes the way we expect characters to interact.
Percy could also react with a sense of determination. Instead of being defeated by the injury, he sees it as a challenge. He starts to figure out what made Artemis hurt him in the first place. If it was a misunderstanding, he tries to clear it up. If it was something more malicious, he starts to plot his revenge. He uses his own wits and the powers he has to either heal himself or find a way to make Artemis see the error of her ways. He might also seek the help of his friends, like Annabeth or Grover, to come up with a plan to deal with the situation.