Maybe they embark on a journey to rescue a captured demigod. Along the way, they face various challenges like crossing a dangerous river filled with sea serpents. Percy's knowledge of the water and his brother's problem - solving skills (again, depending on how the fanfiction portrays him) would help them get through the obstacles.
In some fanfictions, they might go on an adventure to discover the truth about their family. This could involve visiting different gods and goddesses, asking for their help. During this journey, they would learn more about their heritage and the secrets that their parents might have been hiding, and face many perils together.
They could go on a quest to find a powerful artifact that has the potential to destroy both their worlds. Bruce's detective skills and Percy's demigod powers would make them a formidable team. For example, they might have to search for an ancient Atlantean relic that has been corrupted by dark magic.
They could have an adventure in the world of the gods together. Tony, with his scientific knowledge, might try to understand the magic of the gods, and Percy could show him around the places like Mount Olympus. Maybe they would have to team up to stop a powerful enemy that threatens both the mortal world and the world of the gods.
He could have adventures in the sky realm. Maybe he would go on quests with Zeus' other children, like flying on thunderclouds to battle powerful sky - based monsters. He might also get involved in the politics of the Olympian gods, which would be a whole new kind of adventure compared to his usual sea - related ones.
They could go on a quest to find a magical object that has the power to balance the magic in both their worlds. Since Percy is used to dealing with Greek mythology - related quests and Bella has her own experiences in the Twilight world, they could combine their skills. For example, Percy's ability to fight monsters and Bella's immunity to some vampire powers could come in handy.
Maybe they go on a journey to find a lost artifact that has the power to control both vampires and demigods. Along the way, they face various challenges like werewolves who don't want them to succeed and demigod enemies who see Bella as a threat. Percy would use her strategic thinking from her demigod training, and Bella would rely on her instincts from living in the vampire world.
He probably has adventures fighting new and different kinds of monsters. The lightsaber would give him an edge in combat against creatures that are used to more traditional weapons.
He could have adventures involving other sea - related deities. Since Thetis is a sea - goddess, he might interact more closely with her kin. For example, he could be sent on a quest by Thetis to retrieve a powerful artifact from the deep sea that is guarded by a fearsome sea - monster.
They could have an adventure where they have to retrieve a lost artifact that is important to both their parents. Percy could use his ability to control water to navigate through underwater caves or obstacles, while Annabeth's knowledge of architecture and strategy would help them figure out the puzzles and traps along the way.
He could have adventures in London's underground tunnels. There are so many mysterious and spooky areas down there that could be full of monsters. Maybe he'd discover an ancient Greek temple hidden beneath the city that's been forgotten for centuries.
He could have adventures with local mythological creatures. Alaska has a rich Native American mythology, and Percy might encounter spirits like the Raven or the Bear. Maybe he'd find a hidden tribe that has been protected by a local water spirit, and he has to help them deal with some threat to their water source.