Well, it would probably shatter Annabeth. Percy is her closest friend and love. His death would leave a huge void in her life. She might become more withdrawn, consumed by grief. She could also become more determined to carry on Percy's legacy in the fight against the forces they were up against.
One scenario could be that they are facing a powerful monster. The monster is about to strike Annabeth, and Percy jumps in front of her at the last moment, taking the fatal blow. Another possibility is that they are in a dangerous situation like a collapsing building or a sinking ship, and Percy uses his powers to ensure Annabeth's escape while he stays behind and perishes.
Well, if Annabeth dies in a fanfic, it would be a really tragic turn. Percy would be completely devastated. He's been through so much with her, and she's not just his girlfriend but also his partner in all their adventures. Their relationship has been a central part of the Percy Jackson series, so her death would change the whole dynamic. Fans would be heartbroken too, as Annabeth is a very popular character. It could lead to Percy going on a dark path, seeking revenge or just shutting down completely.
On the other hand, she could try to honor Percy's sacrifice. Annabeth might focus on the reasons why Percy died for her and strive to fulfill any tasks or goals that he might have hoped she would achieve. She would carry on his legacy in a positive way, even though she is heartbroken.
Percy would be completely devastated. He might go into a state of shock at first, unable to believe that Annabeth is really gone. Then he could become filled with rage, vowing to take revenge on whoever or whatever was responsible for her death.
It might also be related to some sort of enemy or threat that specifically targets Percy and his relationship with Annabeth. The enemy could be so powerful that Percy realizes the only way to stop it from harming Annabeth is to sacrifice himself, like if the enemy feeds on his life force or his connection to Annabeth, and he chooses to end it by sacrificing his own life.
It could start with Artemis getting into a situation where she's in a vulnerable position. Maybe she's been lured into a place where her powers are diminished. Percy, being a friend and an ally, rushes to her aid. Along the way, he has to fight through hordes of lesser monsters, which takes a toll on him. When he finally reaches Artemis, they are confronted by a really powerful adversary. Percy realizes that the only way to save Artemis is to take the full brunt of the enemy's attack himself. So he does, and that's how he dies.
Annabeth could also be angry, not at Percy but at the situation or the forces that led to his death. She might vow revenge and start on a journey to find out who or what was responsible for Percy's sacrifice and make them pay. This could lead her into a whole new set of adventures and challenges as she tries to come to terms with her loss.
One possible storyline could be that in a battle against a new and powerful enemy, Annabeth sacrifices herself to save Percy. Maybe she steps in front of a deadly attack meant for him, like a powerful magic blast from a primordial being. This would shatter Percy, leading him on a journey of both revenge and self - discovery as he tries to come to terms with her loss.