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 He could become withdrawn and moody, shutting out his friends and allies.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.
At first, Percy could be in denial. He might think that there's some misunderstanding, that Annabeth doesn't really mean to break his heart. So he tries to talk to her, to make things right. But as the truth sinks in, he could be really depressed. He might lose his appetite, not be able to sleep well, and just generally seem like a shell of his former self. His whole world revolved around Annabeth, and now that it's falling apart, he doesn't know how to cope.
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.
He could also become angry. Percy has a bit of a temper, and he might lash out at Annabeth, demanding an explanation. He might feel betrayed, especially if he doesn't understand the real reasons behind the break - up. In his anger, he could distance himself from their mutual friends and go on solo quests to clear his head.
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 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.
Well, it could be that Artemis, in the fanfiction, has to make a choice that goes against Percy's feelings. Maybe she has some divine duty that forces her to break his heart. For example, she might have to sacrifice their relationship to protect her hunters or to maintain some sort of balance in the mythological world.
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.
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.
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.