Dracule Mihawk is the current holder of the title, “Greatest Swordsman in the World”.
True to his epithet, “Hawk Eyes”, Dracule Mihawk has exceptional eyesight, able to easily track Luffy’s high-speed Gear Second movements, and strike with extreme precision, releasing a long-range slash at him while there was a chaotic battlefront of New World pirates and Marine officers between them.
Mihawk’s first demonstration of power was defeating all but one of Don Krieg’s fleet of 50 ships and 5,000 men by himself just before a storm struck. His strength is so great that Don Krieg accuses him of having the power of a Devil Fruit. While it has not yet been confirmed that he does not, the Databooks indicate that his abilities are from pure skill and power.
Mihawk is shown to have a strong will as he was able to resist Luffy’s Haki and be one of the few to still be able fight despite others around him falling unconscious. Perhaps the most accurate and evident demonstration of his incredible power is the fact that he has remained unharmed during the whole series thus far. He also has great mental strength, shown when he is not one of the men to fall for the charms of Boa Hancock while most men easily fall for the pirate empress’ beauty and turned to stone.
Mihawk travels around in a coffin-shaped raft with two green-flamed candles, a single black sail, and a single seat. The fact that he can traverse the unforgiving oceans, as well as the Grand Line itself, in such a meager craft is yet another testament to his abilities.
The fact that Mihawk used to be a rival of one of the Yonko implies that Mihawk might be one of the strongest characters in the series. Infact he has been known to have frequently fought with Shanks when they were younger.
Although he has never been seen resorting to physical combat outside of swordplay, his fortitude suggests that he naturally possesses superhuman strength and resilience, as he applied tremendous strength behind all of his swings, enough to split battleships and a mountain of ice with ease. Additionally, during his duel with Zoro, he was capable of effortlessly defeating a three sword-wielding Zoro with the single “crucifix” knife, his Kogatana, hung around his neck disguised as a pendant, generally used as a dinner knife.
Mihawk demonstrates tremendous dexterity and supreme skill in swordsmanship, especially when using his main sword, Yoru. His range of abilities are extensive, from destroying entire fleets of ships and giant icebergs with immense power to being able to deflect the course of bullets with masterful and graceful precision. He is also able to cut through steel with ease and rapidity, as demonstrated with the steel-bodied Mr. 1, whom even Zoro struggled to beat.
Mihawk taught Zoro how to use Busoshoku Haki to protect his swords from any damage, which not only proves that he himself can use it, but that he possesses mastery and understanding of it to be able to train Zoro to become an extremely skilled Busoshoku Haki user in his own right.
Zoro himself even admitted that even after training with Mihawk during the entirety of the (time-skip), while talking down to Pica, that he (Zoro) is still not anywhere near Mihawk’s level of skill with swordsmanship, further attesting to Mihawk’s combat and fighting prowess. Because of his status as the greatest swordsman alive in the One Piece world, defeating him is Roronoa Zoro’s ultimate goal.