Not Mihawk, Zoro may have to overcome Shiryu to achieve his aspirations.
In One Piece, Zoro's dream is to become the greatest swordsman in the world. To attain that title, he needs to defeat the greatest swordsman, Dracule Mihawk. Everything points to Mihawk being Zoro's final opponent, but perhaps that's not the case.

During their first encounter, Mihawk showed Zoro a significant disparity in their strength. Since being defeated, fans have eagerly awaited Zoro's rematch with Mihawk. However, when they meet again, Zoro set aside his personal ego to seek Mihawk's tutelage. In that sense, Mihawk could be seen as Zoro's mentor.
The enemies the Straw Hat Pirates face are typically nefarious villains, which doesn't quite fit with Mihawk's character.
Currently, Blackbeard and his crew are poised to be the Straw Hat Pirates' ultimate adversaries in the series. Interestingly, within Blackbeard's crew, there's also a formidable swordsman, Shiryu of Rain. He could be Zoro's ideal opponent.

To this day, Shiryu has not yet fully revealed his might, but as one of the 10 captains of the Blackbeard Pirates, this name is undoubtedly formidable.
Shiryu, formerly the chief warden of Impel Down, possesses formidable power and is ranked among the most dangerous and ruthless individuals in the world of One Piece. What makes Shiryu even more dangerous is his current possession of the Suke Suke no Mi, a Devil Fruit of the Paramecia type, granting him the ability to render his body and anything he touches invisible. Thanks to this incredible ability, Shiryu can unexpectedly appear beside his opponents and strike them down effortlessly.
Who knows, in the future, Shiryu may clash with Mihawk, resorting to dirty tactics to defeat the Hawk-Eyed swordsman. This would spark a rivalry between Zoro and Shiryu.
