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'.
He might face mental challenges like PTSD. Tartarus is a horrible place, and the things he witnessed there could haunt 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 challenge could be the lack of the traditional focus for his magic. Without a wand, he might struggle to direct his magic precisely. For example, when he tries to cast a simple levitation spell, he may end up making objects fly out of control.
He might face challenges like mastering new jutsu. The toads have unique techniques that Naruto has to learn, which could be physically and mentally exhausting.
One major challenge could be trust issues. Since the world of espionage is full of double - crossers, Percy might constantly be wondering who he can really trust within the agency and outside. Another challenge could be the physical danger. He could be sent on dangerous missions where his life is at stake, like infiltrating enemy strongholds.
The legal system in some fanfic settings might not recognize slavery as an illegal practice immediately. Anakin would have to fight through bureaucracy and convince lawmakers to change the laws. There could also be cultural acceptance of slavery in certain areas, and Anakin would have to overcome the deeply - rooted beliefs of the people there.
One big challenge could be gaining the respect of the older and more traditional ninja in the village. They might be skeptical of his youth and inexperience. Another could be dealing with political intrigue within the village and from other villages. Since he's young, they might think they can manipulate him.
One challenge could be readjusting to the village life. After intense training in a different environment, the daily routines and social norms of Konoha might seem strange. Also, he may face jealousy from some of his peers who haven't advanced as much in their skills during his absence. Another challenge could be dealing with the new threats that Konoha might be facing, and having to prove himself all over again to the village elders that his new skills are useful for the village's protection.
He might face the challenge of overtraining or undertraining. Since he doesn't have a coach or a training partner to tell him when he's doing too much or too little, he could end up either exhausting himself or not making enough progress. In fanfiction, he could also struggle with loneliness. Training by himself means no one to share his frustrations or small victories with. This loneliness could potentially affect his mental state and in turn, his performance. Additionally, without feedback from others, he may develop bad habits in his training that could be hard to correct later on.
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.