"Talk to the guard of the land's most famous Vault"
In order to do this, you have to complete everything at the vault. Music theater and event scenes should be 100% once beating the story, however multi stage battle objectives are a little bit more involved. This CAN be one of the more time consuming parts of 100%ing the game, and I recommend trying to do as much as possible while playing the story to minimise the grind. Missed multi stage objectives can be seen in the vault, and you can go to the library to replay stages that you missed objectives on (except the last multi stage battle which is always accessed through the normal battle screen). Once everything is done, simply talk to the guard of the vault and this achievement will pop.
A full list of all multi stage battle objectives can be found here:
https://bit.ly/39ZbdLt