There's a possibility that it could be a character who has been misinformed about Annabeth. They might have heard false rumors about her and in a fit of anger, punch her. Or it could be a character who is on a mission to take revenge for something they think Annabeth's group did, and she becomes the target as a representative of that group.
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.
One possible scenario could be that it's a case of mistaken identity. Maybe someone thought Annabeth had done something wrong when she hadn't. Another could be in the heat of an argument where emotions got out of control and someone lashed out at her. Or perhaps it's part of a more complex plot where an enemy is trying to send a message to her friends by punching her.
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 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 close friends would most likely be involved. Percy, for sure. He would probably be worried about her and try to sober her up. Grover might also be there, trying to use his nature - related powers to find some herbs or something that could help her feel better.
Percy might be one. They have a close relationship, and in some fanfictions, he could be more forward with his feelings through flirting.
It could be a new, unknown enemy. Maybe someone from a far - off planet who has a grudge against the Saiyans. This character could be really powerful and sees Gohan as an easy target at first, so he throws a punch.
It could be new girls who come into the camp. They see Annabeth's position and all she has achieved, like her close friendship with Percy and her role as a leader, and they become jealous. Maybe some minor characters who have always been in the background and feel overshadowed by Annabeth.