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.
On the other hand, Percy might be sad. He respects the gods and Artemis is an important figure. Her hatred could make him feel rejected and disappointed. He may try to find ways to redeem himself in her eyes, like performing heroic deeds that are related to her domain, such as protecting nature or her followers.
Percy could also be angry. He's a hero and has saved the world multiple times. He may feel that Artemis' hatred is unjust and he might be tempted to confront her about it, to demand an explanation for her animosity.
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.
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.
Percy is initially shocked. He's used to Artemis being this strong, independent, and in - control goddess. When she loses her memory and her behavior changes, Percy is at a loss. He tries to be patient and understanding, like when she doesn't recognize him or acts in a more child - like way. He feels a sense of responsibility to protect her and figure out what's wrong.
He probably tries to stay calm at first. Percy has been in tough situations before, so he would assess the situation.
He may also try to figure out what went wrong. Percy is a smart demigod, and he would likely not just accept the betrayal without trying to understand the cause. So, he might start investigating, talking to other characters who might have some insight, like the other demigods or even some minor gods who are friendly to him.
She would probably be furious. Artemis has a strong sense of justice and protecting the vulnerable. So, she would likely immediately start to plan how to deal with those responsible for Percy's abuse.
She could also be angry. Given her power and status, she might feel slighted by Percy. She may take some form of revenge, not in a malicious way but perhaps by making Percy's life a bit more difficult during his quests. For example, she could send her hunters to interfere or withhold some information that could be useful to him.
Initially, Percy is likely to be heartbroken. He thought he had a certain relationship with Artemis, whether it was friendship or respect. So when she betrays him for Orion, he may go into a state of self - doubt. He could wonder what he did wrong and start to isolate himself. But as time passes, he may gather his strength and decide to face Artemis and Orion head - on, to either regain Artemis's trust or show her the error of her ways.
In some fanfictions, Artemis might react with intense anger. She is a protector, especially of the innocent. So she could immediately seek justice for Percy, using her power and influence among the gods to find the perpetrator.
Artemis would be in shock initially. Given her status as a powerful and independent goddess, the idea of being forced into marriage is unthinkable. She would likely try to use her divine powers to break free from the situation. If she can't do it immediately, she might start to negotiate. She could offer other things in exchange for her freedom from this marriage. And if Percy shows any sign of taking advantage of the situation, she would not hesitate to put him in his place.