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.
In this fanfiction, perhaps Annabeth getting shot is a turning point for her character. She could start to question her own safety and the safety of those around her. Her friends might go on a hunt for the person who shot her, leading to a lot of action and adventure. It could also lead to some emotional moments between her and her closest friends, like Percy, as they worry about her survival.
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.
Perhaps a mysterious stranger who has some unknown vendetta against the Heartland family. This person could have been lurking around the ranch for a while, waiting for the perfect opportunity to strike. Or it could be someone within the community who has a hidden agenda and sees Amy as an obstacle to their plans.
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.
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 example could be a situation where Annabeth sees Percy getting a lot of attention from a new girl in their group. She might start acting cold towards Percy, which is a classic sign of jealousy in fanfiction. In such a story, the author might explore her insecurities about her relationship with Percy.