If the gods were to interfere with her plans for the hunters without her consent. Artemis is very protective of her hunters and their way of life. Any meddling from the other gods in her domain could easily enrage her in a fanfiction scenario.
There might be a fanfiction where Artemis is angry because of some false rumors spread about the Hunters. She could be on a rampage to find the source of these rumors and in the process cross paths with Percy. Maybe Percy gets caught in the middle and has to help her clear the Hunters' name while dealing with her anger.
I'm not sure if there is specific 'Percy Jackson and Artemis make out' fanfiction that's considered great. Fanfiction can be a very subjective area. Some people might write it for the shock value or just to explore a very different kind of relationship. But it's likely that a lot of die - hard fans of the original series might find it a bit off - putting as it doesn't really align with the characters' personalities as we know them.
One possible plot could be Percy having to defend Artemis from a new and powerful enemy. Maybe a primordial being has awakened and is targeting Artemis. Percy, with his skills and the help of his friends, must fight this enemy. He could also have to deal with the politics among the gods as he tries to protect Artemis, since some gods might not be so happy about his interference.
One reason could be that Percy is loyal to Annabeth. In the original series, his relationship with Annabeth is strong, and he might not want to betray that for Artemis. Artemis is also a virgin goddess, which adds a layer of complexity to any potential relationship.
In this fanfiction, it could be that Artemis is in a situation where she is about to be killed or lose her powers forever. Percy, being the selfless hero he is, takes on a deadly task to prevent that from happening. Maybe it involves facing an ancient and malevolent god who has a vendetta against Artemis, and Percy uses his unique abilities and the element of surprise to try and stop this god, but at the cost of his own life.
One possible reason could be a misunderstanding. Maybe Artemis misinterprets Percy's actions as being against her or her hunters. For example, if Percy accidentally endangers one of her hunters during a quest, Artemis might see it as a betrayal of her trust in him.
Well, it could involve Percy being tasked with protecting Artemis in a way that goes against his normal alliances. Maybe some dark force is after Artemis and Percy has to use his skills in a new and unexpected way.
One possible plot could be that the son of Artemis discovers a threat to the demigod world that is related to his mother's domain. He then seeks out Percy for help because of Percy's reputation. Together, they embark on a journey to find a magical artifact that can stop the threat.
In a 'Percy Jackson adopted by Artemis' fanfiction, perhaps Percy is exiled from Camp Half - Blood due to false accusations. Artemis, who has always been intrigued by Percy's courage, takes him in. With Artemis as his new guardian, Percy gets involved in the Hunters' battles against ancient monsters that threaten the world. He also has to deal with the jealousy of some of the other Hunters who are not happy about a male being in their midst.
Maybe in the fanfiction, if someone on the Argo 2 endangered his friends, Percy would get angry. He's very protective of his friends, like Annabeth. If any harm came their way because of someone's recklessness on the ship, that could set him off.