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 female friends in the series could also be important. They could offer advice, share their own experiences, and be there for her. For example, Piper might use her charm - speak to get her some supplies when they are in a difficult situation. And Hazel could use her powers to help Annabeth if she needs some privacy or something related to her new situation.
A female mentor or an older female friend could be important. This character could provide a different perspective. She might come from a different background or have unique experiences related to menstruation. She could offer Arya wisdom and guidance that her family members might not, like how to handle social situations when on her period or how to embrace this new part of her femininity.
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.
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 fanfiction, Annabeth's quest usually involves a lot of physical activities. Having her period can make these activities more difficult. There's also the problem of dealing with the waste in an appropriate way during the quest. And if she's in a dangerous area, she has to balance taking care of herself and staying safe from the quest's threats.
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.
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's a chance it could be a new character introduced in the fanfiction. Maybe someone who has a mysterious past and enters Annabeth's life briefly but leaves a big impact, resulting in her pregnancy.
Percy might be one. They have a close relationship, and in some fanfictions, he could be more forward with his feelings through flirting.
A mentor - like figure could also be a main character. This could be an older student or a teacher who takes Annabeth under their wing. They could offer her advice, help her understand the unwritten rules of the new place, and guide her through difficult situations. For instance, if Annabeth is in a new school with a complex social hierarchy, this mentor could help her find her place within it.