It could be a new character that is a combination of a dark wizard and a Hollow. This creature would be able to use both dark magic and Hollow abilities. It would target both Hogwarts students and Soul Reapers. Ichigo and Harry would have to figure out its weaknesses, which would be a difficult task as it has powers from two very different universes.
Voldemort could still be the main villain in a different way. Suppose he discovers Tonks' unique connection to Harry and tries to use her as a weapon against him. He could manipulate her mind or put her in dangerous situations to force Harry to make sacrifices or bad decisions.
It could be a dark wizard who has somehow managed to gain the power of Hollows. This antagonist would be extremely dangerous as they would combine the dark magic of the wizarding world with the destructive power of the Hollows. They might be after the cousin because of some special power or connection that the cousin has, which could be used to either rule both worlds or destroy them.
It could be a new character created by the fanfiction author. Maybe a powerful wizard who was once shunned by the wizarding community and now wants revenge by stealing magic.
A dark wizard who has merged the dark arts with Wonderland's magic could be the main villain. He might have created some sort of dark Wonderland where all the creatures are under his control, and Harry has to break this control to restore balance.
Maybe a new character, a Muggle - born wizard who was shunned by both the Muggle and wizarding worlds. This character, out of bitterness, decides to combine Muggle technology and magic to create the droid army and rule over both worlds. He would see Harry Potter and his friends as the main obstacles to his grand plan.
It could also be a dark wizard from the past who has been trapped in a hidden part of Hogwarts and is now released during Harry's third year. This wizard could have a vendetta against the Potter family or Gryffindor house and start causing trouble.
It could be a Death Eater who has somehow made a pact with a powerful force from Scorpian's world. This villain would be extremely dangerous as they'd combine the dark magic of the Harry Potter universe with the unknown and potentially deadly powers from Scorpian's realm.
A possible main villain could be an ancient sorcerer from the new dimension who has been awakened from a long slumber. He's enraged that the wizarding world has been interfering with his dimension's magic, and decides to take revenge on Harry Potter's world. He has powers that are unknown to the normal wizarding world, like the ability to control time in his dimension, which makes him a formidable foe.
It could be an alternate version of Dumbledore. Maybe in this universe, Dumbledore has been corrupted by power and his thirst for knowledge leads him to do dark things. He could be trying to control the entire wizarding world using some powerful and forbidden magic.
Perhaps Bellatrix Lestrange had a secret accomplice who was also interested in the Potter family. After Bellatrix's death, this accomplice decides to hunt down the missing sister to finish what Bellatrix started - destroying the Potter family once and for all.