One challenge could be the complexity of the jutsu itself. His father's jutsu might be very advanced and require a high level of chakra control that Naruto doesn't initially have.
He might face opposition from some in the village. There could be those who think that Naruto isn't ready or worthy to learn his father's jutsu. Also, there could be secrets surrounding the jutsu that certain people don't want Naruto to uncover. Another challenge is that the jutsu might be tied to certain emotions or memories that are difficult for Naruto to handle. For example, if the jutsu was created during a tragic event in his father's life, Naruto has to deal with those emotions while trying to learn it.
Well, in many such fanfictions, Naruto might start learning his father's jutsu when he discovers some hidden scrolls or when a mentor who knew his father decides to teach him. Maybe it could be someone like Jiraiya who reveals some secrets about his father's techniques.
One challenge could be mastering the chakra control required. The Hidden Mist Jutsu demands a precise amount of chakra to create a thick and effective mist. Naruto has had issues with chakra control in the past, so this would be a hurdle. Another challenge might be adapting his fighting style. He's used to more straightforward and aggressive attacks, and the stealthy nature of the Hidden Mist Jutsu would require a different approach.
He might learn a time - traveling jutsu. This would be really cool as it could allow him to go back and change certain events in the Naruto world, or gain knowledge from the past to use in the present battles.
If he learned a healing jutsu, he would become more nurturing. He could use this jutsu not only to heal his friends in battle but also to help the villagers. His reputation would change from just a powerful fighter to also a healer, and he would be more respected in a different way.
One challenge could be controlling the space - time aspect of Kamui. It's a very complex jutsu, and Naruto, who is used to more straightforward chakra - based attacks, might struggle to understand the intricacies of warping space and time.
Maybe he found some hidden scrolls left by his mother. These scrolls could have contained the details of her jutsu. Naruto, being the curious and determined ninja he is, would have studied these scrolls carefully and learned the jutsu.
If Naruto creates a very powerful and dangerous jutsu, some characters might be afraid of him. For example, the villagers who were once suspicious of his Nine - Tails power could again start to fear him. However, his close friends like Sasuke and Sakura would likely trust him and help him control and master the new jutsu.
He could potentially learn the Flying Thunder God Technique. It's a very powerful jutsu that Minato was famous for. Naruto's already fast with his Sage Mode and Nine - Tails Chakra, and this would make him even more formidable in battle.
One challenge could be the complexity of chakra control required for Particle Style. Naruto has always had a bit of a struggle with precise chakra control.
Another challenge is adapting his fighting style. Naruto's existing fighting style is based on his ninja training and the use of chakra. Ultra Instinct is a completely different concept. He has to figure out how to integrate the new power into his attacks and movements without losing his own identity as a ninja. For instance, he can't just abandon his signature Rasengan, but needs to find a way to use it in conjunction with Ultra Instinct abilities.