If you meant entering the Inner City in general, then yes, you need to proceed with the Arena Arc, and for that, you either need to beat all 3 top fighters in the arena, or you need to beat one of them multiple times. I don't remember how many times. Agostino is the easiest to defeat, regardless of build. Jiiji needs some more thought and preparation since that one hits hard with magic. Ubald kind of depends on whether you went full slut or not. If you did, I'm not sure if it's possible to beat him without certain top tier equipment and spells.
That said, there's really no reason to try to do anything than beat Agostino repeatedly tbh, unless you want to see the defeat scenes from the others. No other fight in the game will require the builds and/or item combinations that those latter two require.