Well, it could be about Hiruzen teaching Naruto all kinds of ninja skills from a young age. Maybe he also imparts wisdom and values to Naruto, which makes Naruto grow into a very different ninja compared to the original story. For example, Naruto might be more composed and less of a troublemaker in the village at first because of Hiruzen's strict yet loving upbringing.
Naruto might be more knowledgeable about the history and politics of the village. Hiruzen, being the Hokage, would surely educate Naruto on such matters. This would make Naruto more diplomatic and better able to handle complex village - related issues. He would also be more respectful of traditions and the hierarchy within the village, having been raised by the village's leader.
Maybe Naruto is put in a situation where he feels that Hiruzen's way of handling things is the best option. For instance, if there is a major crisis in the village that requires a more traditional and experienced approach, Naruto might choose to act like Hiruzen. Also, he could be influenced by the stories he has heard about Hiruzen and wants to fill his shoes in a way.
Perhaps in this fanfiction, Naruto has some sort of special power or transformation that he unlocks just in time to face Orochimaru. It could be related to his Nine - Tails chakra in a new and unique way. He uses this power to break through Orochimaru's defenses and save Hiruzen. Naruto might also use his knowledge of Orochimaru's weaknesses that he has learned either from Jiraiya or from his own past encounters with Orochimaru's minions.
In a fanfiction where Naruto is trained by Hiruzen, Naruto would likely have a more traditional and disciplined training. Hiruzen could instill in Naruto the values and ethics of being a true shinobi from the very beginning. Since Hiruzen has seen many great shinobi in his time, he could mold Naruto into a shinobi similar to those of the past. This might mean Naruto would be more proficient in basic ninja skills like stealth and intelligence gathering. Also, his chakra control could be improved more rapidly under Hiruzen's guidance, which would enhance his overall combat capabilities.
The plot might involve Naruto learning about the history and politics of the village from Hiruzen. Since Hiruzen has a wealth of knowledge and experience, he could be guiding Naruto on how to be a great leader in the future, not just a powerful ninja.
One possible plot is that Hiruzen discovers a plot against Naruto by some anti - Uzumaki forces. He then uses his combat skills and his network of spies to stop the threat before it reaches Naruto. He might also place some of his most trusted shinobi to guard Naruto at all times.
Perhaps there are some shinobi within the village who are jealous of Naruto's potential. They might try to harm Naruto in secret, and Hiruzen has to be vigilant against them. These shinobi could be from clans that have rivalries with the Uzumaki or those who just don't want a new powerful force emerging in the village.
One popular 'naruto hiruzen bashing fanfiction' might be those that focus on his decisions regarding Naruto's upbringing. Some fans might write stories where they criticize how Hiruzen let Naruto grow up alone and ostracized in the village. They could explore alternate scenarios where Hiruzen made different choices to better Naruto's life from the start.