One big challenge would be not being believed. People in the past might think he's crazy when he talks about future events. Also, he has to be careful not to change too much and disrupt the whole timeline. Another challenge could be that some of the villains in the past might be more powerful than he expected, and he'd have to find a way to defeat them with his current skills and limited knowledge of the past.
Naruto would face a lot of challenges. Firstly, he'd have to adapt to the different technology and ninja culture of the past. The jutsu and fighting styles might be a bit different. Secondly, he has to deal with the fact that he might accidentally change something that has a huge negative impact on the future. And thirdly, he might not be able to find allies easily. People in the past might be suspicious of his motives and his strange abilities that seem out of place for that time.
Naruto would also have to deal with the physical differences. As a girl, she might not have the same physical strength she had as a boy. This could be a big issue in combat situations, as she would need to adapt her fighting style. Maybe she would have to rely more on agility and strategy rather than brute force.
One challenge would be dealing with students who don't respect his authority. Naruto was always a bit of a rebel himself, so he might find it hard to enforce strict rules. Another challenge could be teaching complex ninja techniques to students with different levels of ability.
She would face the challenge of fitting in. The social norms and ways of life in the past at Hogwarts would be different. For instance, the way students interacted with each other and with the teachers might be more formal or old - fashioned compared to her time.
During the training, Naruto could face the challenge of balancing his own power with Kurama's. It's not easy to incorporate such a powerful and wild source of chakra into his own fighting style. He also has to face the fact that Kurama's training is not going to be easy - going. There will be setbacks and failures, and Naruto has to keep his motivation high. Moreover, Naruto may have to face the jealousy or suspicion of other ninjas who might not understand his new - found power from Kurama's training.
One challenge could be controlling Kurama's powerful chakra. It's so immense that Naruto might struggle not to be overwhelmed by it. If he can't control it well, he could end up harming himself or losing control during the exam.
One big challenge would be finding skilled ninjas to help him. Ushiogakure might not have a large population to start with. He'd need to either train new ninjas from scratch or convince others to join him. Another issue could be dealing with any existing rivalries or feuds in the area.
One major challenge would be the cultural difference. Naruto comes from a world of ninjas with its own set of values, and England has a long - established and very different aristocratic and cultural system. Another would be the political intrigue. The English court is known for its complex power plays, which Naruto, who is used to more straightforward battles, might find difficult to navigate.
He might face opposition from other ninja who fear his new - found power. Some might see him as a threat and try to stop him. This could lead to Naruto having to fight not only his enemies but also deal with the politics and mistrust within the ninja world.
One challenge could be controlling the new power. Just like Naruto had to learn to control the Nine - Tails' chakra, he'd have to figure out how to use Achilles' power without overexerting himself. Another might be dealing with enemies who would target his new weakness, if he has one like Achilles' heel.
The characters would face the challenge of not being recognized or being seen as a threat. If they time - travel to a time when their families or tribes didn't know them yet, they could be considered outsiders. For example, Hiccup might be seen as a strange boy with his un - Viking - like ways of handling dragons. Also, they would have to deal with the different cultural norms of the past. Things like how battles are fought, how the tribe is led, and how resources are shared could all be very different, and they would need to adapt quickly to avoid getting into trouble.