Perhaps an organization from the future that doesn't want Shinn to change the past. They might send their own agents to stop him. These agents could be new characters created specifically for the fanfiction. They would have advanced technology and be highly trained, and their goal would be to preserve the original timeline which is somehow beneficial to their future plans.
It could be a future version of someone who has turned evil due to Shinn's time - traveling actions. For example, if Shinn changes something that causes a once - good character to go down a dark path. Maybe a character who was originally a minor figure in the original story but becomes a major threat because of the altered timeline.
In some cases, it could be Shinn himself from another parallel timeline. This Shinn might have different motives and goals. He could be trying to maintain the original flow of events because he believes that any change would lead to a worse future. So he becomes the antagonist to the Shinn who is trying to make positive changes in the past.
Well, one possible plot could be that Shinn travels back in time to the start of the war. He uses his knowledge of future events to try and prevent certain tragedies. Maybe he tries to stop the development of some of the more dangerous mobile suits. He could also attempt to change the relationships between the different factions, like trying to make the Earth Alliance and ZAFT cooperate more.
It could be a rogue scientist who was once part of the Gundam project. He has his own ideas about how the Gundam technology should be used and is willing to do anything to get his hands on it, even if it means going against Sonia and the Gundam's pilot.
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.
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.
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.