Another possibility is a demigod from the past who is jealous of Percy's knowledge and power. This demigod could be someone who was once in a position of power or influence but feels threatened by Percy's sudden appearance and her attempts to change things. They might try to undermine her at every turn, whether by spreading false rumors about her or directly attacking her when she least expects it.
It could be Zeref. If Natsu goes back in time, Zeref might have different plans or be in a more powerful position at that time. He could be the main obstacle for Natsu to overcome, especially if Natsu is trying to change things related to the dark magic that Zeref wields.
Perhaps an ancient martial arts master who has gone astray. He might envy Kenichi's pure heart for martial arts and tries to corrupt him. This antagonist could use his deep knowledge of ancient martial arts against Kenichi, creating intense battles between them. Also, he might try to use Kenichi to gain more power in his own time period.
It could be a powerful sorcerer from the time she travels back to. This sorcerer might sense that Elena doesn't belong in that time and wants to stop her from interfering with his plans. Maybe he has some dark magic he wants to use to take over the kingdom or town she's in.
It could be Danzo. In the original story, Danzo was a major factor in the Uchiha massacre. If Itachi goes back in time, Danzo would likely still be plotting against the Uchiha. His thirst for power and his extreme methods would put him at odds with Itachi's new attempts to save the clan.
Maybe the main antagonist could be an older version of Madara Uchiha who has somehow found a way to manipulate time as well. He might be trying to change the past in a way that benefits him and his grand plan for the ninja world, which would put him in direct conflict with Jiraiya.
It could be a time - traveling version of Orochimaru. He might have his own plans for the past and Sasuke's interference could put them at risk. So, he tries to stop Sasuke from changing the past in a way that would undermine his future goals.
It could be a time - traveling version of one of his existing villains. For example, Zoom could have found a way to travel back in time and is trying to change history to make his own future more powerful. Another option is that a new character, a time - keeper type of villain, emerges. This villain's goal is to stop Barry from messing with the timeline and will do anything to preserve the original course of history, even if it means harming Barry.
It could be an ancient and powerful Titan who was thought to be defeated long ago. Since Percy is in the past, this Titan could be in his prime and see Percy as a threat to his plans of ruling over the world again. For example, Kronos might be even more powerful in this past era and Percy has to find a way to stop him without the help of his modern - day friends.
Maybe a corrupted past version of a demigod. For example, a demigod who was promised great power by the Titans and turned against the Olympians. This demigod could see Percy as an obstacle to their plans and try to stop him at every turn. They would know the time period well and could use that to their advantage against Percy.
There's a possibility that a new character could emerge as the main antagonist. Ruby's time - traveling could disrupt the normal flow of events, and this might create a new power - hungry or revenge - seeking character. This new antagonist could be someone who blames Ruby for the changes in the timeline and wants to stop her at all costs.