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.
Another challenge might be dealing with the new skills he has to learn. If they are complex or very different from what he already knows, it could be difficult for him. Let's say she teaches him some ancient and forgotten jutsu that require a high level of chakra control which Naruto has to struggle to master.
One challenge could be the physical exhaustion. Jiraiya's training is likely to be very demanding physically, and Naruto might struggle to keep up with the intense workouts.
Chakra depletion is also a big issue. With all the chakra - control exercises and sparring, Naruto could run out of chakra quickly. This would not only limit his ability to practice jutsu but also leave him vulnerable in case of an unexpected attack during training.
One challenge could be mastering difficult jutsus. The Third Hokage might set high standards for Naruto to learn complex techniques, which would be a struggle for him.
One of the main challenges is time management. The Chunin Exams are approaching fast, and Naruto has a lot to learn. He has to quickly grasp complex ninja techniques that Kakashi is teaching. Another biggie is dealing with his own impatience. Naruto is eager to prove himself and might rush through the training, not fully absorbing the lessons.
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 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.
He might face challenges like maintaining order among the chaotic and often unruly denizens of hell. There could be powerful demons who don't want to follow his leadership, and he has to use his skills and wits to subdue them.
Naruto would face the challenge of self - discovery. Being forced into the ninja life, he has to figure out if he can actually find something positive in it. He also has to face the danger that comes with being a ninja. With his initial reluctance, he may not be as prepared as those who willingly entered this path. And there are the political aspects within the ninja world that he'll have to navigate, which can be especially difficult when he didn't choose to be part of it.