He might face mental challenges like PTSD. Tartarus is a horrible place, and the things he witnessed there could haunt him.
In the fanfic, he may also face new threats that are related to his time in Tartarus. Maybe some dark forces from there have followed him out, or there are those who fear what he has become after surviving Tartarus and want to eliminate him.
One challenge could be dealing with the trauma. Tartarus is a terrifying place, and Percy might have nightmares that disrupt his school life. He could also find it hard to relate to his classmates who have no idea what he's been through.
One possible plotline could be Percy having nightmares about his time in Tartarus. He might struggle with PTSD, which could affect his relationships with his friends and family at Camp Half - Blood. Another could be that he brings back some sort of dark power or knowledge from Tartarus that he has to figure out how to control or use for good. Maybe he discovers a way to close the entrance to Tartarus permanently so that no more monsters can come out and endanger the demigod world.
The environment itself is a big obstacle. Tartarus is a place of extreme darkness and chaos. It can mess with Percy's mind, making it difficult for him to focus on his training. The terrain is also treacherous, with rivers of fire and bottomless pits.
Perhaps he could make an alliance with some of the less hostile creatures in Tartarus. There might be beings who are also tired of the chaos and want to help Percy in exchange for something, like a promise to free them from Tartarus if he ever gets the chance. Percy is known for his charisma and ability to make friends, even in the most unlikely situations.
He might face terrifying monsters. Tartarus is full of the most dangerous creatures in the Percy Jackson universe. So he'd have to fight for his life constantly.
One challenge could be the language difference. Even though English is spoken in both places, the accents and some local slang in England might be confusing for Percy. For example, he might struggle to understand what people mean when they use terms like 'bloke' or 'cheeky'.
One major challenge could be the powerful and malevolent creatures that inhabit Tartarus. Monsters like the Titans or other ancient evils would try to stop him. They are much stronger than the usual foes he faces on the surface. Another challenge is the very nature of Tartarus itself. The place is designed to be inescapable, with its dark magic and chaotic environment constantly working against Percy.
In some fanfics, Nico di Angelo could be the one to help Percy. Since Nico has a connection to the Underworld and has some dark powers, he might be able to enter Tartarus more easily than others. He could use his powers to fend off the monsters and guide Percy to safety.
Percy might struggle with his new identity. He has been a demigod for so long, and suddenly becoming a primordial god means he has to re - evaluate his place in the world. He may miss his old life, his friends, and the simplicity of being a demigod. Adjusting to the new powers and responsibilities is not going to be easy.
Some of the more powerful and vengeful spirits in Tartarus could be the main antagonists. These spirits could possess demigods or mortals close to Percy to get to him. They might be angry that he escaped their domain and want to drag him back. Additionally, there could be a group of rogue demigods who believe that Percy has been corrupted by Tartarus and they see it as their duty to stop him, even if it means becoming his enemies.