In some fanfictions, Artemis may hurt Percy because of her strict sense of justice. Say Percy breaks one of her rules unknowingly, like entering a sacred forest she has marked off. Artemis, being the goddess of the hunt and protector of the wild, might feel the need to punish him. This could lead to Percy getting physically injured, like being struck by one of her arrows. Or maybe Artemis is under a curse that makes her act out of character and she ends up hurting Percy without really meaning to. This then sets off a chain of events in the fanfiction where Percy has to deal with the injury and also try to find a way to break the curse on Artemis.
One common plotline could be Artemis constantly interfering in Percy's relationships with others. For example, she might try to keep him away from Annabeth. Another could be her being overly protective of Percy during his quests, which might cause some tension with the other gods or demigods who are used to Percy acting independently. And sometimes, there could be a sub - plot where Artemis' possessiveness makes Percy question her motives and his own role in her actions.
One common plotline could be Percy, as a vampire, being drawn to Artemis's power and purity. Maybe he starts off as a threat to her but then falls in love. Another could be Percy being an outcast among vampires and finding an unexpected connection with Artemis, who is also an outsider in some ways among the gods.
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.
One possible plotline could be that Percy sacrifices himself to save Artemis from a powerful and ancient enemy. Maybe there's a prophecy that foretells his death in order to protect her. Another could be that Percy is tricked into a situation where he has to give his life for Artemis to prevent a great disaster from befalling the world of the gods. And perhaps in his death, he becomes a symbol of heroism that changes the way the gods view demigods.
Perhaps a plotline where Percy, as the daughter of Artemis, is chosen for a special mission. The gods, seeing her unique heritage, task her with something that no other demigod can do. It could be related to restoring balance in the world of the gods. Along the way, she has to deal with her own insecurities about not being a 'normal' demigod and prove herself worthy of the mission.
Another plotline might involve Artemis teaching Percy some of her hunting skills. This would be an interesting reversal as Percy is usually the one with his own unique powers. He could learn about tracking in the forest and using a bow and arrow more effectively from her. In turn, he could teach her about the sea and its secrets. It would be a great exchange of knowledge and skills between the two.
One possible plotline could be Artemis having to deal with her new - found feelings while still maintaining her role as a goddess. For example, she might struggle between her duties and her attraction to Percy. Another could be Percy being completely unaware at first, leading to some comical misunderstandings. Maybe he thinks Artemis is just being overly friendly in a mentor - like way.
One possible plotline could be Percy going through some sort of extraordinary adventure that changes Artemis's view of him. Maybe he saves her in a way that no one else could, and this new - found respect and connection gradually turns into love, leading to their marriage.
One possible plotline could be that Percy has been wronged by Artemis in some way, perhaps she made a decision that put Percy or his friends in danger, and now he's out to punish her by thwarting her plans. For example, if Artemis made a deal with a villain that backfired on Percy's team, Percy might seek revenge.
One common plotline could be Hinata choosing someone else over Naruto, which deeply wounds him. Another might be Hinata lying to Naruto about something important, causing him emotional distress. There could also be a plot where Hinata physically harms Naruto in a moment of being controlled or influenced by some external force.