Mihawk is one of the most powerful pirates to appear so far, possessing an immense amount of skill in battle.
Mihawk once saw a strong rival in Shanks. Their battles were said to shake the whole of the Grand Line and Mihawk often sought Shanks out for duels. Whitebeard praised their battles as legendary.
Mihawk currently holds the title of “Strongest Swordsman in the World”. There’s no unknown swordsman who’s secretly stronger than him. This also suggests that Mihawk is atleast equal to Shanks.
He traveled the world alone fighting every strong swordsman he could find, until there was no one left. His last obstacle before becoming the World’s Strongest Swordsman was a Yonko-level swordsman. After Shanks retired, there was no one left, so he got the title. He couldn’t become a Yonko because he was alone, he had no territories or armies of crewmates.
According to the One Piece Vivre Card Databook Mihawk is waiting for someone stronger than Shanks to one day appear. The implications of this statement are pretty important. If he was weaker than Shanks, then someone on Shanks level would be more than enough for him. He wouldn’t look for someone stronger. If he was on his level, an idea that his duels with Yonko Shanks would support, then it would make sense he would want someone stronger.
I think this information pretty much confirms that Mihawk is Yonko level. It also heavily suggests that Mihawk = Shanks, and that Zoro will beat Mihawk when he surpasses Shanks. Thoughts?
*Theory by 4FunRegion