Friendship is also a big theme. Even though Percy is Artemis' guardian, they develop a friendship. This friendship is often tested by outside forces or misunderstandings. Some fanfictions focus on how they overcome these issues and strengthen their bond, which makes for some really heartwarming and engaging stories.
A powerful Titan who has escaped from Tartarus could be the main antagonist. He might be seeking revenge on Artemis for her role in the previous battles against the Titans. This Titan could have new and terrifying powers that make him a formidable foe for Percy and Artemis.
One great 'Percy Guardian of Artemis' fanfiction is 'The Guardian's Quest' on FanFiction.net. It has an interesting plot where Percy has to face various challenges while protecting Artemis. The author does a wonderful job of describing the action scenes and the relationship between Percy and Artemis.
One key element is the relationship between Percy and Artemis. It's often a complex dynamic, mixing respect, distrust at times, and mutual admiration. For example, in some fanfics, Percy has to earn Artemis' trust as he is a male in her domain which is usually female - only.
One idea could be Percy having to protect Artemis from a new and powerful monster that has a special ability to track her. Another could be Percy and Artemis teaming up to retrieve a lost magical artifact that is important for the balance of the world. Maybe Percy has to enter Artemis's domain in the forest and face challenges there while protecting her.
There's also 'Percy and Artemis: A New Alliance'. In this fanfic, Percy teams up with Artemis to face a common enemy that threatens both the mortal and immortal worlds. It delves deep into their personalities and how they learn to work together despite their differences.
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.