So in the anime several adventurers reached level 6. Which is the level one of the protagonist of the story (Aisu) has. Is this the highest level an adventurer has reached in the story? Which adventurer has the highest level?
It's "Champion" Otar of Freya Familia, he is the only level 7 in Orario
Ains said it in Danmachi: Sword Oratoria - chapter 34: Bell Cranell
As for comment of Joe W:
Yes, Ottar is not the only level 7 in the world based on the Danmachi fanbased Wiki about Ottar. But based on discussion who is the other level 7, it seems it is not introduced yet even in the light novel version