It could be a time - traveling sorcerer who wants to change history for his own evil purposes and sees Achilles as a threat. The sorcerer might try to stop Achilles from getting back to his own time or use his knowledge of the future to his advantage against Achilles.
The main antagonist could be Agamemnon. In the original story, he and Achilles had a lot of conflict. In this fanfiction, if Achilles is fighting for Troy, Agamemnon would still be leading the Greek forces against him. His thirst for power and glory would make him a formidable foe, constantly devising strategies to defeat Achilles and take Troy.
It could be a time - traveling villain who is trying to disrupt the timeline for their own gain. This villain might be trying to erase certain events or people from history to change the future in a way that benefits them.
A time - traveling bounty hunter could be the main antagonist. He might be after Lucy because she has somehow disrupted the time - space continuum. He's cold - hearted and will stop at nothing to bring her to some time - traveling justice.
Perhaps an ancient evil that was sealed away long ago but is released due to Temari's time - traveling disruptions. This evil entity then starts causing chaos in the past, and Temari is the only one who can stop it with her modern skills and knowledge.
It could be a time - traveling villain from the future who wants to change the past to gain more power in their own time. They might try to stop Naruino from achieving their time - travel goals.
It could be a dark wizard from the past who has the power to manipulate time. This wizard might see Natsu and Mira as threats to his plans to change the past for his own evil gains. He would try to stop them from interfering with his time - related schemes.
Dr. Wily would be a very likely main antagonist. He could be using time travel to his advantage, for example, going back in time to steal important technology before Dr. Light discovers it. This would give him an even greater edge in his evil plans in the present or future.
It could be an alternate - version of Tony Stark from a different timeline who has gone rogue. This version might have different values due to the differences in his timeline's history and is now causing problems in the main Stark's timeline.
Maybe a time - traveling collector. This character travels through different times collecting rare items or memories. When Lincoln enters a particular time period, the collector sees Lincoln's unique family situation as a valuable item to collect and tries to keep him trapped in that time, away from his own family.
Shego could also be the main antagonist. Maybe she discovers a way to time travel on her own and decides to go back in time to eliminate Kim before she becomes a threat. Kim would have to follow her through time to prevent this and save her younger self.