It could be that the Akatsuki, if they still exist in the fanfic's plot, would be antagonists. Even with Naruto being trained by Kaguya, they might have goals that conflict with Naruto's new - found power and purpose. And they might try to stop him from achieving whatever it is he's aiming for under Kaguya's training.
The Otsutsuki clan members other than Kaguya could be antagonists. Since Kaguya is training Naruto, they might see Naruto as a threat to their plans.
One potential antagonist could be those who fear Naruto's new - found godlike powers. There might be ninja from other villages who see Naruto as a threat to the balance of power. Another could be remnants of Kaguya's old enemies who resurface, seeing Naruto as a continuation of Kaguya's influence and wanting to stop him. Also, there could be dark forces within the ninja world that want to corrupt Naruto's new powers for their own evil purposes.
There could be new antagonists created specifically for this fanfic. Maybe some dark forces that were sealed away by Asura long ago are awakened. They would oppose Naruto because they see him as a threat to their resurrection or their evil plans.
It could be some rogue shinobi who are after Pakura's knowledge. Since she's training Naruto, they might see it as an opportunity to get to both of them and steal their techniques. Maybe they were once her enemies or just power - hungry individuals.
Orochimaru could still be an antagonist. He might see Naruto as a threat especially if Kakashi is training him intensively. His goal of obtaining power could lead him to target Naruto.
The Akatsuki could still be the main antagonists. Even with Naruto getting trained by Mangetsu, the Akatsuki's goals of collecting the tailed beasts would still pose a major threat to Naruto and the ninja world.
The Akatsuki could still be the main antagonists. Even though Sasori is training Naruto, the rest of the Akatsuki might view Naruto as a threat and try to eliminate him. Also, Orochimaru could be an antagonist. He might be interested in the new skills Naruto is learning from Sasori and try to steal them for his own experiments.
The Akatsuki could still be the main antagonists. Even with Naruto's training by the Kyuubi, they would be after the tailed beasts. Their goals of collecting all the tailed beasts would put them in direct conflict with Naruto. And they have some really powerful members like Pain and Itachi.
Well, in such a fanfic, Naruto might gain some extremely powerful and unique abilities. Kaguya being his trainer could mean he'd learn ancient and forbidden jutsus. Maybe he'd also gain a deeper understanding of the chakra and the origin of the ninja world.
Sasuke could be a side character. Since Naruto is getting special training from Kakashi, Sasuke might feel jealous or motivated to train harder himself. Sakura could also be there, perhaps she tries to learn from Kakashi's training methods to help Naruto better. Another potential side character could be Iruka, who might check on Naruto's progress from time to time and offer some words of encouragement.
It could be the other Hidden Villages. Since Naruto is becoming so powerful under Danzo's training, they might see him as a threat and try to stop him. Maybe they would send their best ninjas to take him down.