Perhaps they time travel to a period when a great evil was first emerging. They then have to figure out a way to stop this evil from taking root without using the knowledge and power they have in their own time. This could involve finding and training local ninja in the past to fight against this new threat, and in the process, they learn new techniques and strategies that they can bring back to their own time.
A plot twist could be that Naruto discovers a secret about Tsunade that she has been hiding all along. It could be something related to her family or a power she has been suppressing. This discovery could either strengthen their relationship or create a rift between them. Also, there could be a twist where an outside force tries to use their relationship to gain power in the ninja world. They might try to manipulate Naruto or Tsunade to their advantage.
One possible plot twist could be that the baby has some unique power that neither Naruto nor Tsunade possess. Maybe it has the ability to control time, which causes all sorts of chaos and also attracts the wrong kind of attention from villains who want to use the baby's power for their own evil deeds.
One possible plot twist could be that Naruto's Mokuton abilities attract the attention of Orochimaru. He might try to capture Naruto to study his unique power. Since Tsunade raised Naruto, she would be extremely protective and engage in a fierce battle with Orochimaru to keep Naruto safe. This would not only test Tsunade's strength but also Naruto's growth under her care.
One possible plot twist could be that Naruto, when he travels back to graduation, realizes he has some of his future skills and knowledge. He might use this to outperform everyone in the exams in unexpected ways, like using advanced jutsu that no one has seen before, which would shock his classmates and teachers.
One possible plot twist could be that Tsunade trains Naruto not just in physical combat like she did with others, but also in medical ninjutsu. This would be unexpected as Naruto is more known for his brute force. Maybe Naruto uses his new medical skills in a creative way during a battle, like healing his opponents to show mercy and then defeating them when they are off - guard.
In the fanfiction, Tsunade might rescue baby Naruto from a dangerous experiment that was being carried out on him. As she rescues him, she realizes that Naruto has an extraordinary ability to resist the negative effects of the experiment. This leads her to believe that Naruto is destined for something great and she devotes herself to protecting him at all costs.
One possible plot twist could be that since they are the same age, Naruto might become Tsunade's rival in the medical ninjutsu field. Naruto, with his determination, could develop his own unique style of healing that challenges Tsunade's traditional methods. This could lead to a friendly competition between them, which in turn would force both to improve their skills and knowledge.
Perhaps a plot twist would be that there is some sort of curse associated with Naruto's lineage as their grandson. This curse could be related to the same forces that Tsunade and Jiraiya fought against in their lives. Naruto has to struggle not only with his normal ninja duties but also with this hidden curse. It could manifest in strange ways, like affecting his chakra control or making him a target for certain enemies. On the other hand, it could also be a source of great strength if he can overcome it. And there could be a prophecy related to him being the grandson of Tsunade and Jiraiya that he has to fulfill, which adds another layer of complexity to the story.
One possible plot twist could be that Naruto and Tayuya travel back to a time when the Hidden Leaf Village was first founded. This would put them in the middle of the early power struggles and they might have to use their future knowledge to prevent a great disaster. For example, they could stop a rogue ninja from stealing important village secrets that could have changed the course of the village's history.
One possible plot twist could be that their time travel messes up the existing timeline in ways they didn't expect. For example, they might accidentally prevent important events from happening in the past that were crucial for the future they came from. Another could be that they find out they were meant to time travel all along to fix a long - hidden problem in the ninja world's history.