Percy might be one. They have a close relationship, and in some fanfictions, he could be more forward with his feelings through flirting.
There could also be new or original characters created in the fanfiction who are attracted to Annabeth's intelligence and beauty and thus flirt with her. These characters could be designed specifically to add a new dynamic to the story and see how Annabeth responds to the attention from someone outside her usual circle.
Percy could be one. He might flirt with her in a more playful, inside - joke kind of way. Like he'll make references to their shared adventures and say something like 'You know, you were really cute when you were fighting that monster back there, Annabeth. And you're even cuter now.' It's a light - hearted and affectionate form of flirting that's based on their deep bond.
Well, it depends on who is flirting with her in the fanfiction. If it's someone she doesn't like, she'll probably be dismissive and give cold responses. However, if it's someone she has a bit of an interest in, she could be coy and a bit shy while still maintaining her confident facade.
Some fanfictions might have a more mature or experienced demigod flirting with Annabeth. Maybe a guy who has been on many more quests than her and uses his stories and adventures to impress her. Or it could be a character who is known for his good looks and confidence, like a son of Aphrodite, who tries to use his natural charm to flirt with Annabeth.
Maybe an antagonist who wants to disrupt the group dynamic. If Annabeth is a key part of a group, punching her could cause chaos and confusion among her friends. It could also be someone who has been influenced by dark magic or some sort of mind - control in the fanfiction. This would make them act against their normal nature and punch Annabeth without really having a personal grudge.
Percy would probably be an important character. He's Annabeth's close friend and love interest. His reaction to Annabeth getting her period could be interesting, like he tries to be supportive but is a bit clumsy at first.
Her family could be a great help. If they are aware of the situation, they can step in. Maybe her parents can talk to the school authorities or even directly to the bullies' parents. Family support is always crucial in such situations.
In this fanfiction, Natasha Romanoff could be a great ally for Annabeth. Natasha is a skilled spy and fighter, and Annabeth has her own set of combat and survival skills. They could bond over their shared ability to assess situations quickly and make smart decisions in the heat of battle. Also, Natasha might be interested in Annabeth's knowledge of different cultures and mythologies which could potentially help in their missions.
Maybe it's a human who has somehow discovered the world of demigods and is afraid of their existence. They shoot Annabeth out of fear and misunderstanding. Another option is that it's a rogue demigod who has gone bad and is working against their own kind. This character could have a personal grudge against Annabeth specifically, perhaps because of her intelligence and leadership skills which they envy.
It could be an enemy from the underworld. Maybe a powerful demon or a vengeful spirit that has a grudge against her. They might use their dark powers to harm her, like sending a bolt of dark energy her way.
There might be some new characters introduced in the fanfiction who have different ideals or motives that clash with Annabeth's. These new characters could be the antagonists as they oppose Annabeth, and Percy has to step in. For example, if they think Annabeth's way of handling a certain quest is wrong and Percy believes in her, he'll fight against their ideas.