He probably tries to stay calm at first. Percy has been in tough situations before, so he would assess the situation.
At the start, Percy could be shocked that he's been captured by Artemis. But then his survival instincts kick in. He might start bargaining with Artemis. He could offer to help her in some way in exchange for his freedom. He would also be thinking about his friends and how they could come to his rescue. Percy would likely be observing everything around him, from the behavior of Artemis's hunters to the layout of the place. And he'd be constantly formulating plans in his head to either escape or turn the situation around so that he's in control.
He would likely be angry. Percy has a temper, and being betrayed by someone he thought was an ally would fuel his rage. He might lash out verbally or even physically, depending on the situation. For example, if they were in a battle together and Artemis suddenly turned on him, he would have to defend himself while also dealing with the emotional turmoil of the betrayal.
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.
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.
Percy might be devastated. He could become withdrawn and moody, shutting out his friends and allies. He might also be filled with anger and a sense of betrayal, which could lead him to make rash decisions.
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.
Percy may initially resist with all his might. He's a strong - willed character. But as he realizes that fighting against it might not be the best option for the moment, he could start to observe Artemis more closely. He might learn from her, like how she handles her power and her connection to nature. However, there would always be an underlying sense of unease and a longing for his own world. He may also try to communicate with his friends secretly, hoping they can find a way to get him out of this situation.
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.
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.
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.
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.