One challenge could be mastering the balance between different elements. Each element has its own characteristics, and it's not easy to control them all harmoniously.
One challenge could be controlling the intensity of the ice. If he makes it too cold or creates too much ice, it might harm his friends or the surrounding environment. For example, if he's in a room and loses control, he could freeze everything and everyone in it.
One challenge could be the basilisk's own will. Even if Harry has the ability to control it, the basilisk is a powerful and ancient creature with its own instincts. It might resist Harry's control from time to time, especially when it comes to situations that go against its natural behavior, like being made to not attack innocent students.
The environment could also pose a challenge. If he's in a really hot place, using his ice - controlling ability might be much more difficult as the heat could quickly melt the ice he creates. Also, if he's in a place with very little water vapor in the air, it would be hard to form ice in the first place, which limits his power usage.
One challenge could be the strength of the enemy. If the enemy is very powerful, it would be difficult for Aang to overcome them alone. Another challenge might be the lack of resources. He may need certain items or help from others to save the Airbenders but not be able to get them easily.
One challenge could be controlling it. Haki is a different kind of power compared to chakra, so Naruto would have to learn how to regulate the flow and intensity of his haki. For example, if he uses too much haki at once, it might drain him quickly.
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.
One challenge could be Naruto's appetite. Naruto loves to eat, so Kakashi would have to constantly find food to satisfy him. Another is Naruto's hyperactivity. Keeping Naruto still and focused on one thing would be tough for Kakashi.
One challenge could be dealing with the traditionalist teachers and pure - blood families. They might resist any changes Harry tries to make as they are used to the old ways. For example, if Harry wants to introduce muggle - born friendly policies, some of the old - school pure - bloods might oppose it.
One major challenge could be Fenrir's own distrust. As a werewolf, he may have faced a lot of prejudice and be very wary of Hermione's intentions. Another challenge might be the lack of existing knowledge about werewolves. Even though Hermione is very knowledgeable, there are still many mysteries about werewolves that could make it difficult to find a proper solution.
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.