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.
Harry may have a hard time learning new spells. In the wizarding world, most spells are taught with the use of a wand. Without it, he has to find alternative ways to learn and practice. He might need to experiment a lot more and could potentially put himself in dangerous situations while trying to figure out how to perform spells without a wand.
He also has to deal with the secrecy around wand - making. Since it's a highly guarded art in the wizarding world, he might face opposition from the Ministry of Magic or other wizards who think he's meddling in something he shouldn't. Plus, he has to make sure that the wand he crafts is unique to him and suits his style of magic, which is no easy feat.
In such a fanfic, he might rely on natural elements more. For example, he could draw power from the earth, water, air or fire. By connecting with these elements on a deep level, he can use their inherent magic. He may touch a tree and transfer its life force into a spell, or use the flow of a river to create a protective barrier.
One challenge could be resistance from the existing authority. There might be some teachers or administrators who don't want to give up their power easily. They may see Harry as too young or inexperienced.
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 challenges like mastering new jutsu. The toads have unique techniques that Naruto has to learn, which could be physically and mentally exhausting.
Well, one of the challenges could be the manipulation by dark forces. Some fanfics might depict dark wizards trying to use the Tournament to harm Harry. They could try to rig the tasks against him. Another problem could be his own self - doubt. With so much pressure, he may start to question his abilities. And the tasks themselves may require new spells or skills that he has to quickly learn, like a particularly difficult form of magic for the second task in the lake.
The Dementors are a huge challenge. Their presence alone can drain his happiness and will to escape. He has to find a way to avoid them or protect himself from their effects.
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.
He might face mental challenges like PTSD. Tartarus is a horrible place, and the things he witnessed there could haunt him.
Politics within Asgard could be a challenge. There may be different factions or groups who have different opinions about allowing an outsider like Harry to become a member. He might have to navigate through these political intrigues and gain the support of key figures in Asgard, like Thor or Odin, in order to finally become a member.