Perhaps a group of dark wizards from both the Harry Potter world and Byakko's world who have joined forces. They want to create a new order where they rule over both magical realms. They see Harry and Byakko as obstacles to their plans. This group could be made up of some of the most devious characters from both universes, and they use a combination of dark magic and the unique powers of Byakko's world against Harry and his newfound friends.
A dark wizard from the Harry Potter universe could be the main antagonist. Maybe a follower of Voldemort who escaped the final battle and found his way to Byakko's world. He sees the power of Byakko and wants to use it for his own evil purposes. He could try to enslave Byakko and use its power to take over both the wizarding world and Byakko's realm.
It could be a power - hungry alien leader who wants to take over Hogwarts and use its magic for their own empire.
Most likely, Medusa would be the main antagonist. Her ability to turn people to stone makes her a very dangerous foe for Harry Potter and the other characters in the wizarding world.
It could be a dark fairy who wants to use the power of both the wizarding world and Pixie Hollow for her own evil purposes. She might try to steal the magic from Hogwarts and the pixie dust from Pixie Hollow to become all - powerful.
Maybe the main antagonist could be Ra's al Ghul. He's always interested in power, and if he got his hands on some magic from the Harry Potter universe, he could become an even greater threat. He could try to use the magic to bring about his vision of a 'perfect' world, which would be at odds with both Harry's and Nightwing's ideas of justice. So they'd have to join forces to stop him from achieving his goals.
It could be a descendant of a rival family to the Peverells. This person might be jealous of the power and secrets that the Peverell family held and wants to stop Harry from uncovering them. They could try to manipulate events to their advantage and create obstacles for Harry.
It could be Aku. Since he is the main villain in Samurai Jack's world, his power and evil nature would make him a great antagonist. He could see Harry's magic as a threat and try to eliminate him. And if he teams up with some of the dark forces from the Harry Potter universe like Voldemort or the Death Eaters, it would be even more challenging for Harry and Jack.
There could be a group of dark wizards who are working together to bring chaos to the wizarding world. They target Amelia Bones because of her position in the Ministry and Harry Potter because of his fame. This group, with their evil intentions and powerful dark magic, would serve as the main antagonists in the fanfiction.
The main antagonist might be a being from another dimension who is able to manipulate both magic and the Hulk's gamma - irradiated energy. This being wants to use the chaos caused by the meeting of Harry and the Hulk to open a portal to let in more of his kind to take over all the universes. He sets traps for Harry and the Hulk and constantly tries to keep them from working together to stop him.
Perhaps a rogue Overwatch agent who has turned against the organization. When Harry arrives, this agent sees an opportunity. He believes that by using Harry's magic, he can take over Overwatch and rule the world. So he tries to manipulate Harry and turn him against Tracer and the rest of the good - hearted Overwatch members.
One possible plot could be that Harry Potter, during one of his adventures in the Forbidden Forest, stumbles upon a magical portal that transports him to the world where Byakko exists. Byakko, being a powerful and mysterious creature, initially sees Harry as a threat. But as Harry shows his kind heart and magical abilities, they form an unlikely alliance. They could team up to fight a common enemy, perhaps a dark wizard who has also found his way into Byakko's world and is causing chaos there.