A former experiment of Orochimaru's who has escaped and now wants to test his newfound powers on strong opponents. He sees Kakashi and Naruto as prime targets, especially since they are part of the elite ANBU. He has some strange and dangerous jutsu that he uses to try and defeat them.
Perhaps a powerful shinobi from another village who has a special grudge against the Leaf's ANBU. He targets Kakashi and Naruto specifically because of their reputation within the ANBU. He has unique abilities that pose a great challenge to them, like the ability to nullify ninjutsu for short periods.
The main antagonist could be an old - school ninja who believes in the traditional and often harsh ways of the ANBU. They see Naruto's actions as weakening the village and set out to oppose him at every turn, trying to bring back the old ANBU regime.
It could be a rogue Anbu member. This person might be jealous of Naruto's power and popularity within the Anbu. So, they spread false rumors about Naruto which lead to his decision to leave the village. This antagonist would then try to further harm Naruto while he's outside the village, using their own Anbu skills against him.
One option for the main antagonist could be a secret organization that has infiltrated Konoha. They target the Anbu prodigy because they fear the prodigy's abilities could expose their existence and plans. This organization might have members with unique and dangerous abilities themselves. They would constantly send assassins after the prodigy and try to create chaos in Konoha to keep the Anbu and the prodigy distracted while they carry out their real objectives.
It could be an evil shinobi who wants to capture the Kitsune Anbu for their unique powers. Maybe they want to use those powers to take over the Hidden Leaf Village. Another option is a rogue Anbu member who has turned against the village and sees the Kitsune Anbu as a threat to their own plans.
It could be a rogue ANBU member who has gone bad and is trying to expose Naruto's secret identity for some evil purpose.
It could be a powerful rogue ninja who has a vendetta against Kakashi and sees his daughter as a way to get revenge. This antagonist might try to use her as a bait to lure Kakashi or Naruto into a trap.
Perhaps an old enemy of Naruto's who resurfaces and decides to target his family. This could be someone who was defeated by Naruto long ago but has now grown stronger and wants to cause harm to his loved ones. They might also see Kakashi as a threat in protecting the family.
One potential main antagonist could be an older, power - hungry shinobi who has infiltrated the Anbu in the past. This shinobi could be jealous of Naruto's sudden rise in the Anbu (due to his future knowledge) and sees him as a threat. He then starts to plot against Naruto and the Anbu's new - found positive direction. Or perhaps it's a corrupt politician in the village who uses the Anbu as a tool and doesn't want Naruto to change the Anbu's loyalty from him to the village as a whole.
Characteristics of 'Naruto Anbu Kakashi fanfic' include a focus on Kakashi's unique fighting style within the Anbu. His use of the Sharingan in secret operations is often highlighted. These fanfics also tend to explore the darker side of the Naruto world that the Anbu has to deal with. The fanfic might also show how Kakashi's experiences in the Anbu shape his later actions and decisions as a sensei and a member of Team 7. For example, his strictness and high standards for his students might be related to his Anbu training.
One great 'Naruto Kakashi Anbu' fanfic is 'The Anbu Chronicles'. It delves deep into Kakashi's time in the Anbu, exploring his relationships with other members and how his experiences shaped him. It has some really cool action scenes and character development that stays true to the Naruto universe.