Perhaps their daughter is accused of a crime she didn't commit within the demigod community. She then has to prove her innocence while also dealing with the pressure of being the daughter of two very well - known heroes. Along the way, she uncovers a conspiracy that threatens the safety of all demigods.
One possible plot could be that in their dreams, they see their daughter growing up in a world where the threats they faced are no more. She is strong and confident, trained in the ways of the demigods. They dream of her making friends easily at Camp Half - Blood and having a special bond with the nature spirits there.
One possible plot could be that Percy and Annabeth find a hidden underwater city that was once part of Atlantis. They have to solve a series of puzzles and face off against sea monsters to unlock the secrets of the city. The city holds the key to a powerful weapon that could either save or destroy the world of the gods.
She could be a strong and intelligent girl, just like her parents. Maybe she has Percy's sea - green eyes and Annabeth's blonde hair. She might inherit Percy's ability to control water to some extent and Annabeth's strategic thinking.
Maybe there would be some initial tension between Percy and Annabeth's daughter. She could be rebellious and not want Percy interfering in her life at first. But as time goes on, they could form a strong bond. They might go on a quest together, where Percy has to save her from a dangerous foe, and that's when their relationship really starts to grow and develop into a more trusting and loving one.
Her adventures could start right in her own backyard, so to speak. She might discover a hidden entrance to an ancient labyrinth in her neighborhood. As she explores it, she has to use her wits and any powers she has. Later, she could be drawn into a larger adventure where she has to stop an evil force from awakening an ancient and powerful Titan. She would travel across the country, or even across different continents in the demigod world, encountering various mythical beings. Some might be friendly and offer her help, while others would try to stop her at all costs. And through all these adventures, she would grow in strength and wisdom, just like her parents did before her.
One possible plot could be about their journey of preparing for the baby. Percy might be worried about protecting his family from the various threats in their world, while Annabeth could be focused on creating a stable home environment. They'd also have to deal with the reactions of their friends like Grover and the other demigods.
One possible plot could be Percy and Annabeth adjusting to college life while also dealing with new mythological threats. Maybe they have to take on a monster that is hiding in the college library, using their demigod skills and the knowledge they gain from their classes.
One possibility could be that they are in a school setting where they have to wear uniforms. Percy might constantly be getting in trouble for not following the uniform code properly, like having his tie askew or his shirt untucked. Annabeth, being more organized, tries to help him out. This could lead to some comical moments as well as deeper conversations about fitting in and following rules.
Well, perhaps Percy takes Annabeth on a quest to a special location, like an ancient Greek ruin they've always wanted to explore. During this adventure, he finds the perfect moment when they're alone and surrounded by the beauty of the place to pop the question.
It could be a beach day scenario. Maybe they are having a day off from their adventures and just relaxing on the beach in their bikinis and swim trunks, enjoying the sun and having some light - hearted conversations.