One possible plot could be that Artemis is captured by some powerful ancient enemy, like a primordial being. Percy, with his skills and courage, embarks on a quest to find her. He might face various challenges and monsters along the way. Maybe he has to solve some riddles related to the moon, as it's Artemis's domain. Finally, he locates Artemis and uses his water powers in a creative way to defeat the captor and free her.
Maybe Artemis sees Percy's potential. Percy has shown great courage and skill in other situations, and Artemis might recognize that he could be an important asset in the future battles against the forces of evil. So, she decides to save him from Gabe, who is a nuisance and a threat to Percy.
One common plot element is Percy facing some sort of powerful enemy or threat that has captured Artemis. This could be a new, never - before - seen monster in the Percy Jackson universe.
One possibility is that Artemis has been misinformed. Some enemy of Percy has tricked her into thinking that Percy is a danger to the demigods. So she kidnaps him to stop him from causing harm. But as she keeps Percy captive, she slowly realizes that she has been deceived when Percy starts to explain his side of the story and the real threats he has been fighting against.
One possible plot could be Percy getting caught in one of Artemis' hunts by accident. They initially clash due to their different natures but gradually develop feelings for each other.
A plot could be that there's some sort of dark magic that is affecting the balance between the gods and the demigods. Artemis and Percy are brought together to combat it. Along the way, Percy shows a side of himself that Artemis is drawn to. His courage and selflessness intrigue her. And in a moment of vulnerability, Artemis kisses Percy. This kiss then becomes a catalyst for a deeper exploration of their relationship and the greater threat at hand.
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.
I haven't actually read this specific fanfiction, so I can't summarize the exact plot. But generally, it might involve Percy being in a very dark and suicidal state, and Artemis somehow intervenes. Maybe she uses her powers or her wisdom to show Percy that there are reasons to keep living, like the importance of his friends, his potential to do great things in the future, or the value of his own life in the grand scheme of their fictional world.
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.
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.
The plot might involve a prophecy that somehow links Percy and Artemis. This prophecy could bring them together in a journey across different realms. Along the way, Percy discovers a new side of Artemis, one that is not just the cold and distant goddess. Artemis, too, sees Percy's loyalty and selflessness. Their relationship evolves as they face numerous challenges and obstacles, and they realize that their love is something that is fated and cannot be ignored.