It could be an ancient dark magic artifact. The artifact has a hold on Bellatrix, and in a way, it's the 'enemy' that Harry has to defeat to save her. The artifact might be trying to use Bellatrix to carry out some dark plan, like opening a portal to a world full of dark creatures. Harry has to figure out how to break the connection between Bellatrix and the artifact while also fending off the artifact's attacks.
A new dark wizard or witch could be the antagonist. This new dark force might see Bellatrix as a tool or a threat. If they see her as a tool, they'll try to keep her under their control and prevent Harry from saving her. If they see her as a threat, they'll try to eliminate her. Harry then has to not only save Bellatrix but also deal with this new threat to the wizarding world.
It could be some dark wizards who want to use the centaur's parts for potions. They might be following some ancient, dark magic recipe that requires centaur hair or hooves. So they hunt down the centaur, but Harry gets in their way.
In a 'Harry Potter Saves Bellatrix' fanfiction, perhaps Bellatrix is in a situation where she's about to be killed by other Death Eaters who think she's a liability. Harry, having a sense of justice and seeing the potential for redemption in her, steps in to save her. He could then try to show her the error of her ways, using his own experiences of losing loved ones to Voldemort's ideology. Bellatrix might initially resist, but gradually come to understand Harry's point of view.
It could be a dark wizard who has his eyes on Cintra's powerful magical artifacts. He wants to use them to gain more power and is willing to destroy Cintra to get them.
It could be a rogue Death Eater who has escaped from Azkaban. This Death Eater might be desperate to regain his power and believes that unicorn blood will give him the strength he needs. So he sets out to capture a unicorn in the Forbidden Forest, which is where Harry comes in to stop him.
A group of dark creatures like Dementors could be the antagonists. They might be after the young goblin because goblins have a unique life force that can sustain Dementors in a way other prey cannot. Harry Potter would have to face his own fears while using powerful Patronus magic to drive the Dementors away and save the goblin.
It could be a dark wizard who has a vendetta against goblins. This wizard might see goblins as a source of power or wealth and wants to enslave them. So when Harry tries to save the goblin, this dark wizard becomes the main obstacle.
It could be a rogue Death Eater who wants to take over Voldemort's position and sees Harry and Bellatrix's new - found alliance as a threat. For example, a Death Eater who was always jealous of Bellatrix's closeness to Voldemort.
Perhaps a dark wizard from the Harry Potter universe who has heard about the Cullens' unique vampire abilities and wants to harness that power for himself. He could be a follower of Voldemort who escaped the final battle and is now looking for new ways to gain power. So he targets the Cullens, thinking their powers can help him rule both the wizarding and vampire worlds, and Harry has to stop him.
Maybe a new character could be created as the main antagonist. A dark wizard who has infiltrated the Capitol and is using the Hunger Games as a means to create chaos and destruction. He could be more powerful than Voldemort in some ways and would be a great challenge for Harry and Katniss to overcome.
In the fanfic, Bellatrix might use her magic to protect Harry from his abusers. Maybe she realizes the wrongness of the abuse and decides to be his unexpected savior. She could use her dark magic skills to intimidate those who harm Harry, creating a sort of dark - but effective - protection around him.