The Joker could be a great antagonist. He might have captured Robin for his own twisted games and is holding him hostage in some elaborate death - trap. The Young Justice team would then have to outwit the Joker to get Robin back.
Slade could be the main antagonist. He has a history with Robin and might see this as an opportunity to get back at the Young Justice team. He could have lured Robin away and is now using him as bait to draw the rest of the team into a trap. So the team has to deal with Slade's devious plans while trying to rescue Robin.
Well, in this fanfiction, perhaps Robin left because of some misunderstanding with the team. The Young Justice team then starts to recall all the great things he did for them. They search everywhere, from Gotham to other far - flung places. They might even encounter new allies or enemies during their search for Robin. As they get closer to finding him, they also start to resolve the issues that led to his departure in the first place.
A new, original character could be created as the antagonist. Maybe a powerful and vengeful assassin who has a grudge against Robin for some past event. This character could have unique abilities and a personal vendetta that drives the conflict in the fanfiction.
The most obvious antagonist could be the Joker. He loves to torment Batman, and kidnapping Robin would be a great way to do that. He might have some elaborate plan to break Batman's spirit by harming Robin.
It could be a new villain who has a grudge against the Justice League. Maybe someone whose family was affected by the League's actions in the past. This villain would be very smart and powerful, creating elaborate traps for the League members.
The Riddler could be a great antagonist. He might have a grand scheme that not only affects Gotham but also has implications for the Justice League's interests. His riddles could stump both Robin and the League members, forcing them to work together to decipher his plans.
There are several reasons. Firstly, Robin brought a certain energy to the Young Justice team. He was full of enthusiasm and determination which was inspiring. Secondly, his backstory and connection to the wider DC universe, especially through Batman, were great sources of plot ideas. So in fanfiction, having him back means more exciting storylines can be created. His character also had a lot of room for growth, which fans love to explore in their fanfiction.
Obviously, the main character would be the one who would become Robin. But there could also be other important characters like his trainers or guardians. For example, an old martial arts master who taught him the ways of combat.
Maybe a villain from the dimension where Wally has been. This villain could have followed Wally back to seek revenge or to take over the world that Wally has come back to. Since Wally has some knowledge about this villain, it would be his responsibility to stop the villain and protect his friends and the world. The villain might have powers that are a match for Wally's, making it a really tough fight.
The League of Shadows could be a great antagonist. They might see Young Justice as a threat to their plans in the world and Batgirl as an obstacle in Gotham. They could try to manipulate situations to make Young Justice and Batgirl turn against each other while they carry out their own devious plans, like releasing a dangerous virus in a major city.
It could be a powerful sorcerer. This sorcerer might be trying to capture the Ghost Girl's essence for his own dark magic. He sees her as a source of great power because of her unique ghostly nature.