Another possibility is that Naruto has mastered a time - based jutsu. This would be a completely new concept in the Naruto universe. With this jutsu, Naruto could either slow down time for Kakashi while he moves at normal speed, or he could skip forward in time to avoid Kakashi's attacks and then counter - attack when Kakashi is off - guard.
Perhaps Naruto has developed a form of chakra sensing that is far more advanced than Kakashi's. This would allow him to predict Kakashi's moves better and counter them effectively. He could sense Kakashi's chakra flow and know exactly when and where to strike.
Naruto could have the ability to control a new type of chakra nature, like lightning in a more powerful way than Kakashi. This would give him an edge in combat as he could combine it with his Rasengan or other techniques.
It could also be possible in fanfiction that Naruto beats Kakashi through sheer strategy. Naruto has grown to be a very intelligent fighter. He could devise a plan that plays on Kakashi's weaknesses. For instance, Kakashi is often cautious, and Naruto could use that against him. Naruto could set up a series of decoys and traps that lead Kakashi into a situation where he is at a disadvantage, allowing Naruto to emerge victorious.
In a future Naruto and Kakashi fanfiction, Naruto could gain the ability to communicate with all living things. This would help him in understanding the needs of the village and the surrounding nature. Kakashi, on the other hand, might develop a new Sharingan ability that allows him to see the future in a very limited way, like seeing the next move of his opponent a few seconds in advance. This would enhance his combat skills significantly.
Perhaps Naruto is under the influence of some sort of ancient and uncontrollable power. This power makes him extremely aggressive and strong. Kakashi tries to stop him but is no match for this new - found strength of Naruto. As a result, Naruto beats Kakashi senseless. Another plot could be that Kakashi is injured before a fight with Naruto and Naruto, not realizing how badly hurt Kakashi is, uses his full strength and ends up beating him senseless.
With the Rinnegan, Naruto might gain the power of the Human Path. This would allow him to read minds or rip out souls, which is a very dark and powerful ability that would be quite different from his usual positive - natured powers.
Well, considering the popularity of the Naruto series and the creativity of its fans, it's very probable that there is a 'naruto beats kakashi fanfic'. Fans often like to play around with power dynamics and character relationships in fanfics. They might write such a story to show Naruto surpassing his mentor in a battle, which could be an interesting take on the characters' development.
He might gain better chakra control. Kakashi could teach Naruto how to precisely manage his chakra, allowing him to perform jutsus more efficiently and for longer periods. For example, Naruto could use his Shadow Clone Jutsu without exhausting his chakra so quickly.
Maybe Naruto has discovered a new powerful jutsu that Kakashi isn't aware of. This gives him an edge in the fight and he manages to defeat Kakashi.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
Naruto might gain the power of shikai and bankai. Shikai is the first release of a zanpakuto's power, and bankai is the ultimate form. Naruto, with his determination and strong will, would strive to master these forms. Shikai could give him new attacks and defenses, while bankai could make him an extremely powerful force. For example, his bankai could combine his ninjutsu skills with the zanpakuto's power in a unique and devastating way.
Naruto could gain the ability to manipulate light and darkness, which are often associated with Keyblades. This would be a huge change from his normal chakra - based abilities. He could also use the Keyblade to fly, giving him an advantage in both mobility and combat. Another new ability might be the power to heal, as some Keyblades have restorative properties.