Another possibility is that an old enemy of Naruto's from his own world follows him to Ruby's world. This enemy, seeing Naruto getting stronger under Ruby's training, decides to stop them. They might team up with some of the local villains in Ruby's world to create more trouble for Naruto and Ruby.
It could be someone from Ruby's world who doesn't like the idea of her training an outsider like Naruto. Maybe a powerful mage or a warlord who sees Naruto as a threat to their power or the balance of their world.
It could be someone from Guts' world who follows him into Naruto's world. Maybe one of the Apostles. They are powerful and evil beings. Their presence in the Naruto world would be a huge threat and could be a great antagonist as they would have powers that are different from what Naruto is used to dealing with.
It could be Orochimaru. Since he's always after power and Naruto, with Itachi's training, would become a more appealing target. Orochimaru might see Naruto as a threat to his plans of obtaining all the jutsu in the ninja world.
It could be a powerful dark wizard who wants to control the dragons and sees Naruto as a threat because of his newfound dragon - trained powers.
It could be a powerful Grimm - like being that has evolved beyond the normal Grimm. This antagonist might have the ability to think and strategize like a human, making it a much more dangerous foe for Ruby and her team. It could be leading the Grimm attacks in a more organized way, targeting specific areas to cause maximum chaos.
It could be a rogue ninja from a forgotten clan. This ninja might have a vendetta against Naruto's village and has powers that are difficult to counter. So, Naruto has to train to kill him to protect everyone.
Perhaps an ancient evil spirit that was sealed away long ago in Naruto's world but gets awakened by Ruby Lemon's presence. This spirit has the ability to possess people and use their skills for its own ends. It starts to cause chaos in the ninja villages and targets Ruby Lemon and Naruto specifically, seeing them as the key to either its complete destruction or its total domination.
Another option could be a group of pirates who believe that the Ruby of the Sea can lead them to a great treasure. They constantly try to capture the Ruby and the Jester has to fend them off to protect her. The pirates would be a constant threat throughout the fanfic.
The main antagonist could also be a new character created specifically for the fanfic. This character could be an ancient evil that has been waiting for an opportunity to corrupt a powerful Huntress like Ruby. They would then use Ruby's newfound evil nature to further their own dark plans, and Weiss, Blake, and Yang would have to face both Ruby and this new threat.
In a 'naruto trained by ruby' fanfic, perhaps Ruby could introduce Naruto to some unique combat styles. Maybe Ruby has her own set of skills like some kind of magic or special weapon techniques. She could teach Naruto how to combine his chakra with these new elements. For example, if Ruby has some sort of elemental magic, Naruto could learn to infuse his Rasengan with that magic for a more powerful attack.
The Organization in the Claymore world could be the main antagonist. They already have a lot of secrets and do some morally ambiguous things. If Naruto shows up and starts changing the status quo, like teaching Claymore warriors to be more independent, the Organization might see him as a threat and try to eliminate him.