One common theme is the struggle between light and dark within Percy. His transformation into a darker version of himself often creates internal conflict. Another theme is the relationship between Percy and Artemis, which can be complex and filled with tension as they come from different backgrounds and have different natures.
One great 'Dark Percy and Artemis fanfiction' could be 'Dark Percy's Ascent'. It explores Percy's journey into a darker version of himself while interacting with Artemis in a complex and engaging way. The author does a wonderful job of portraying the internal struggle within Percy and the dynamic between him and Artemis.
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.
The Hunters of Artemis are very likely to show up. They are Artemis's loyal followers and would surely be involved in the search for their mistress. Annabeth could also be there. She's Percy's friend and has great wisdom, which could be useful in devising a plan to save Artemis. Grover might be another character. His ability to sense things could help in tracking Artemis or finding clues about her whereabouts.
Maybe Artemis is on a hunt when she stumbles upon Percy. She might be initially cautious, as she's a goddess and Percy is a demigod. She could question him about his presence in Texas.
One reason could be the popularity of Percy as a character. Fans might be more inclined to write about him in a dominant role because they like him better. So, they create fanfictions where he dominates Artemis.
Perhaps a story where Percy is chosen by the Fates to mediate between Hestia and Artemis. There has been some sort of misunderstanding between the two goddesses. Percy, with his charm and unique perspective, tries to get them to see eye to eye. He arranges meetings in different places - sometimes in Hestia's warm and cozy domain, and other times in Artemis's wild and untamed forests. Through Percy's efforts, they not only resolve their differences but also realize that they can work together for the greater good.
In some fanfictions, Percy could be made Artemis' son for creative and often unique plot twists. Fanfiction allows for a lot of creative liberties, so it's not unheard of. However, in the original Percy Jackson lore, there's no such relation.