One Piece has always contained deeper, mythical layers in its story, and Zoro's path is perhaps the clearest example. The Straw Hats are now on a land tied to Norse Myth, Elbaph. The mysteries behind its Three Realms: Heaven, Sun, and the Underworld, could ultimately connect Zoro's path to its conclusion.
Each of his swords appears to correspond to a realm, implying the idea of conquering the Three Realms. If Elbaph's mythos is truly informing Zoro's path, then it may become clear how he completes his vow of becoming the King of Hell.
Disclaimer: The article is a speculative theory and includes spoilers from the One Piece manga.
How Zoro will become the King of Hell in Elbaph in One Piece, explained

Elbaph's mythology could be pivotal in establishing Zoro's true path in becoming the King of Hell in One Piece. The giant's land is inspired by Norse mythology and also has the characteristics of the Three Realms: Heaven, the Sun World, and the Underworld. These are oddly representative of Zoro's three swords.
This example indicates that Zoro's journey as the world's strongest swordsman may not just be one of swords, but Zoro conquering the realms of life, death, and divinity.
Each of the three swords is representative of one of these mythological realms. Enma, the sword that drains the haki of the bearer, signifies the Underworld. This is tied to Zoro stating he would become the King of Hell is rooted in Japan's Enma Daio, the ruler who judges the dead and makes decisions about immoral souls. Wado Ichimonji is tied to Kuina's memory and Zoro's promise to be the end of her journey to become the world's greatest swordsman, thus fitting into Heaven.

Zoro states he will make a name for himself that reaches even Heaven, showing that Zoro hopes to remember Kuina's name and prove to the heavens that he will make it to the ultimate heights. The last sword, Sandai Kitetsu in its chaotic and cursed nature, could mean Sun World, the mortal world where there lies imperfection, balance, and struggle.
This framework reflects Oden Kozuki's journey, whose two swords separated Heaven and Hell. Zoro, on the other hand, has three swords, indicating that he overtakes Oden’s fate in some sense; the fates of Heaven, Hell, and Earth combined.

The mythological connection becomes even stronger when fans consider Kaido's attack, "Three Realms: Ragnarok," which is pulled from the twilight of the gods from Norse mythology. By marking Kaido's body with his Nine-Sword Style, Zoro has inadvertently re-staged the Norse Nine Worlds from Yggdrasil, representing that Zoro's operation is much more elemental than an exercise of swordsmanship.
Elbaph might thus be the arena where these concepts converge. If Zoro is to really be the King of Hell, he might not only master the nature of every kingdom with his swords but also battle against the people who personify them, like Nusjuro and his deathly imagery-bound freezing slashes. Conquering Heaven, Sun, and the Underworld would make Zoro balanced between myth and reality, completing both his promise to Kuina and his own destiny.
Final thought
The mythology of Elbaph may eventually frame Zoro's ascent as not simply a swordsman but the symbolic conquest, where each sword represents one of the realms. Collectively, they are all headed toward harmony and balance in Zoro's range of death, life, and God.
If Elbaph events unfold this way, Zoro's vow to Kuina and his title of King of Hell, take on the possibility of being much more fully realized, mythologizing his evolution beyond the contextual significance of One Piece.
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