One challenge could be dealing with campers of different skill levels. Some might be total beginners while others think they know more than they do.
He may also face the challenge of limited resources. There might not be enough proper swords or training areas for all the campers he has to teach. Also, in some fanfictions, there could be a lack of time as he has other duties at the camp too. He has to balance teaching sword fighting with other tasks like leading quests or participating in camp events.
One challenge could be that the connection between them is being blocked. Maybe some dark magic or a powerful enemy has created a barrier. So Percy has to find a way to break through this block just to get his call for help to Poseidon. Another challenge might be that Poseidon is preoccupied with his own problems in the underwater world, like dealing with a rebellion among his own sea creatures. So Percy has to convince Poseidon that his situation is also important.
One challenge could be his own reputation. Since Fenrir is often seen as a dangerous werewolf, other characters might not trust him around Hermione, which could make it difficult for him to carry out his protection duties effectively.
One challenge could be the public perception. The wizarding world may not be very accepting of Hermione raising Voldemort's daughter. There could be a lot of fear and suspicion. Another challenge is Delphini's own nature. Since she has Voldemort's blood, she might have some inborn dark tendencies that Hermione has to constantly fight against. Also, Hermione would have to deal with the memories and legacy of Voldemort that might be a part of Delphini's upbringing.
One challenge Naruto might face is Gaara's past traumas. Gaara has been through a lot of pain and isolation, which has made him distrustful. It would be difficult for Naruto to break through those barriers and get Gaara to open up. Another challenge could be the political situation. Suna and Konoha have had their differences in the past, and some in Suna might not be happy with Naruto's influence on Gaara. Naruto would have to deal with any potential political unrest or opposition from those who don't trust Konoha.
Naruto would likely struggle with Hinata's shyness. He is a very outgoing person, and suddenly being in a body that is naturally more reserved could be difficult. For instance, when interacting with other characters, he might accidentally come across as too forward or too quiet, which could lead to misunderstandings. Also, Naruto would have to deal with Hinata's personal relationships. Her friends and family know her in a certain way, and any changes in behavior due to Naruto's possession could cause concern or confusion among them.
Well, they might face challenges related to their own powers. For example, Percy's powers over water might be limited in a dry desert area where there is no water source nearby. Thalia's lightning might attract unwanted attention from other powerful beings. Also, there could be internal conflicts. Maybe Percy and Thalia have different ideas on how to best protect Nico. Percy might want to keep Nico hidden, while Thalia thinks it's better to train Nico to fight. And, of course, there are the external threats like powerful and intelligent monsters that can strategize against them.
Another challenge is that without a proper teacher, he may not fully understand the nuances of magic. Magic in the Harry Potter world has a lot of rules and ethics. Harry might accidentally break some of these rules while trying to teach himself. Also, he may not be aware of the proper pronunciation or wand movements for some spells, which could lead to ineffective casting.
Snape and Lucius might be too proud to take instructions from Harry. Since they are used to being in positions of authority, they may not be very receptive to Harry's teaching at first.
One big challenge could be competition among other researchers. In the fanfiction world, there could be rival marine biologists who want to be the first to discover something new. Percy might also face environmental threats. Things like pollution ruining the habitats he's studying or climate change affecting the behavior of the marine life he's researching. He'd have to find ways to work around these issues to continue his work.
He may face challenges in the magical realm. The magic in the Percy Jackson universe might not interact well with his cyborg parts. For example, if he tries to use his powers while his cybernetic parts are active, there could be some unforeseen consequences. Also, he may be an outcast in both the human world (because he's a demigod) and the demigod world (because he's now a cyborg), which could lead to a lot of emotional and practical difficulties.