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.
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.
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 be angry. Percy might lash out at those who betrayed him, feeling a deep sense of injustice. He would probably be determined to prove his innocence and get revenge on those who wronged him.
He might be extremely angry and feel a deep sense of hurt. After all he has done for Poseidon and the gods, being betrayed would shatter his trust. He could go into a period of self - exile, distancing himself from the demigod world and trying to find his own path without the help of his father.
Perhaps Percy would try to understand the primordial's reasons for the betrayal. He's a smart and empathetic character. He might think that there was some misunderstanding or that the primordial was forced into it. So, instead of immediately retaliating, he could try to communicate with the primordial to clear things up. If that doesn't work, then he would be more likely to take a defensive stance rather than an offensive one, at least until he fully understands the situation.
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.
Percy might initially be in shock. He has always trusted Hestia, so when she betrays him, it would be a huge blow. He could become very angry and feel a sense of deep betrayal. He might lash out at those around him, or he could go into a state of self - doubt, wondering what he did wrong to make Hestia turn against him.
At first, Percy could be in shock. He can't believe that the gods, whom he has served and trusted, would betray him. But then, as the reality sinks in, he might become determined to get justice. He starts to plan his next moves carefully, using his wits and the skills he has learned over the years. He may also feel a sense of sadness and loneliness, as he realizes he is now on his own against the powerful gods.