Madara Uchiha would be a formidable foe. His power level is extremely high in the original story, and in this fanfiction, Naruto's speed would be put to the test against Madara's overwhelming strength and various powerful jutsu. Madara might underestimate Naruto's speed at first, but soon realize that he has to take it seriously to avoid being caught off - guard.
Sasuke would still be a likely opponent. Even though Naruto has enhanced speed, Sasuke has his own unique abilities like the Sharingan which can predict movements to some extent. Their battles would be even more intense, with Naruto's speed against Sasuke's strategic use of his Sharingan and ninjutsu.
Kakashi could also be an opponent. He would be a very challenging one, using his vast knowledge and experience. He might teach Naruto some chess strategies during the game, just like he teaches him ninja techniques.
Shikamaru is an obvious choice. Shikamaru is a master strategist, and shogi would be right up his alley. He would give Naruto a really hard time with his complex strategies and deep understanding of the game.
Sasuke could be a great opponent. Their rivalry could translate well into a game of chess. Sasuke's calculating nature and sharp intellect would make him a formidable adversary for Naruto, and their games could be intense battles of wits.
Other villages' leaders or powerful ninjas who don't believe Naruto is ready to be a Kage. They might try to test him or even plot against him during diplomatic meetings before the summit, seeing his new position as a potential weakness in the balance of power.
Often, it's powerful villains like Orochimaru who make a comeback in fanfiction. Naruto has to use his growth and new abilities to defeat him once and for all.
Another could be Kaguya Otsutsuki. However, in the fanfiction, she may return in a more powerful form. Maybe she has found a way to break free from the seals completely and has amassed even more power from other dimensions. Naruto, being abnormally strong, would still have a tough time fighting her as she is one of the most powerful characters in the Naruto lore.
Often, he overcomes powerful villains like Madara Uchiha. In some fanfictions, Madara might be even more powerful than in the original, but Naruto's newfound abilities allow him to defeat him. Another could be Orochimaru, who might have some new and dangerous experiments, but Naruto is still able to stop him.
His opponents could include some of the samurai from the Land of Iron. They are known for their kenjutsu skills. Since Naruto is now a kenjutsu master in the fanfiction, there could be some sort of misunderstanding or rivalry that leads to battles between them. And, of course, there could be new villains created specifically for the fanfiction who are also masters of kenjutsu and pose a great threat to Naruto.
His father, Minato, could be one. Maybe there's some time - travel or alternate reality situation where Minato has been corrupted in some way and Naruto has to fight him to set things right.
The Akatsuki as a whole could be the opponents. Imagine Naruto facing multiple Akatsuki members at once in a fight. The combined threat of their different powers and their goals of capturing the tailed beasts could be overwhelming for Naruto. They might use underhanded tactics, like threatening to kill captives or using mind - control techniques on Naruto's friends. All of these things could make Naruto go insane as he battles against them, trying to protect what he loves.