It could be a powerful ninja - demon hybrid. This antagonist could be jealous of the bond between Naruto and Inuyasha. He wants to use their combined power for his own evil purposes. So, he tries to turn them against each other first by spreading false rumors and then by attacking their loved ones.
Maybe Kaguya from Naruto's world and Naraku from Inuyasha's world team up. They see Naruto and Inuyasha as a threat to their plans of total domination. They use their knowledge of both worlds to create traps and illusions to stop Naruto and Inuyasha from uniting their powers. They also send their minions to attack the two brothers at every opportunity.
It could be a powerful ninja who has become corrupted by the idea of the descendant's powers. He wants to steal those powers for himself to gain ultimate control over the ninja world. Maybe he has a deep - seated envy of the unique combination of abilities the descendant has.
It could be a powerful ninja from Naruto's world who has been corrupted by the Juubi's power and somehow ended up in the Inuyasha world. He wants to use the power of the demons in the Inuyasha world to make himself even stronger and take over both worlds.
Perhaps another reborn character could be the main antagonist. Say, an evil sorcerer from the past who was also reborn in the Inuyasha world at the same time as the OC. This sorcerer has his own agenda of ruling the world and sees the OC as a threat to his plans, especially if the OC is getting in the way of his attempts to gather the Shikon Jewel fragments.
It could be a powerful ninja who wants to capture the fox brother for his own purposes. Maybe he believes that the fox brother's powers can be used to take over the ninja world. This antagonist might be from a rival village or a secret organization within Naruto's own village.
A new demon that thrives in dark and stormy conditions could be the main antagonist. This demon could be attracted to the negative energy of the storm and decides to target Inuyasha. It might have unique powers, like being able to control the lightning in the storm to attack Inuyasha.
One possible plot could be that Naruto discovers he has a long - lost brother who is Inuyasha. They meet in a strange dimension where the worlds of Naruto and Inuyasha collide. Naruto, being his usual self, wants to understand his new - found brother and tries to bond with Inuyasha. Inuyasha, on the other hand, is initially skeptical but gradually warms up to Naruto as they face common enemies together in this new merged world.
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.
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.