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.
Well, perhaps in this fanfiction, Artemis betrays Percy for Orion due to a prophecy. There could be a prophecy that states that Orion and Artemis together will bring about some great change or prevent a huge disaster, and Artemis believes she has to choose Orion over Percy to fulfill it. Also, Orion might have some sort of leverage over Artemis that forces her to turn her back on Percy.
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, she could betray Percy by revealing his secrets to his enemies. Maybe she's forced to do so under some kind of magical compulsion or threat.
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.
Some fans might be really shocked. They are used to seeing Artemis as a more or less benevolent figure, so this sudden betrayal would be a big twist. They'd probably be eager to read more to find out the reasons behind it.
Percy could lose trust in the gods completely. After Artemis' betrayal, he might feel that he can't rely on any of them anymore.
He probably tries to stay calm at first. Percy has been in tough situations before, so he would assess the situation.
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.