Madara Uchiha could be a great antagonist. His powerful Sharingan abilities and his grand plans for the Naruto world would put him at odds with Supergirl. He might see her as a threat to his control and try to manipulate or defeat her. Another option could be Kaguya Otsutsuki. Her god - like powers and desire to reshape the world would clash with Supergirl's values and her attempts to protect the people of the Naruto universe.
Danzo Shimura could be a very interesting antagonist in this fanfiction. He is a shadowy figure with his own agenda in the Naruto world. He might view Supergirl as a wildcard that could disrupt his plans for power and control. He could try to use underhanded tactics like blackmail or assassination attempts against her. And if we consider someone from Supergirl's side of things, perhaps a Kryptonian criminal who has also ended up in the Naruto world could be an antagonist, causing chaos and trying to use the Naruto world's resources for his own gain while Supergirl tries to stop him.
It could be an evil ninja from Naruto's world who somehow gains Kryptonian - like powers. He becomes power - hungry and decides to take over both the Naruto world and Supergirl's world. His knowledge of ninja techniques combined with super strength and other abilities would make him a formidable foe.
Lex Luthor could be a great antagonist. He could be jealous of their combined power and try to create a device that can split them up or weaken their powers. He might also try to turn the public against them by framing them for crimes they didn't commit.
Lex Luthor could be her main antagonist. He might see Dark Kara as a threat to his own plans of world domination. He could try to manipulate her into doing his bidding or, if that fails, find ways to destroy her. Another option is Brainiac. Brainiac might be interested in studying Dark Kara's new form and powers, and in the process, they could end up in a battle as Kara resists being his experiment.
Hinata could be one of the main characters. Since she has deep feelings for Naruto in the Naruto universe, she might follow him into Supergirl's world. Also, Kara's friend Lena Luthor could be involved. She is a complex character and her interaction with Naruto could add an interesting dynamic to the story.
It could be someone from the Naruto universe who doesn't like Naruto's newfound fascination with Aku. For example, Danzo might see Naruto's interest in Aku as a threat to the stability of the village and try to stop Naruto from further exploring Aku - related things. So, Danzo could be the main antagonist in this case.
A fallen angel who is jealous of Lucifer's newfound friendship with Supergirl and his life on Earth. This fallen angel decides to cause destruction on Earth to get back at Lucifer and also sees Supergirl as a threat to his plans of ruling over the mortals.
Lex Luthor could be a great main antagonist. He could be jealous of their combined power and see them as a threat to his plans of world domination. He might create some high - tech weapons specifically designed to counter their abilities.
Maybe a new character could be introduced as the main antagonist. This character could be from a hidden village that has been secretly observing Naruto's growth. They realize his potential as a weapon and plan to steal his power or use him to start a war against other villages.
Krampus himself could be the main antagonist. Since he is a figure known for punishing the naughty, his actions in the Naruto world might be seen as unjust. He could be going after ninjas without really understanding their motives, causing a lot of trouble for the main characters.
It could be a rogue ninja who also has somehow acquired bankai - like powers. This antagonist might be jealous of Naruto's newfound abilities and wants to prove that he is the stronger one. So he starts causing chaos in the ninja world, challenging Naruto at every turn.