Make the bagel an item. (Very important.)
Just keep adding characters as time goes by as well as other DLC. (Fou-Lu from Breath of Fire 4 would be my choice, but I'm sure many don't know him.) This is a game that I can see being constantly updated with a dedicated player-base.
Allow for players to register their own tournaments (or have different tournaments you can choose from). So that instead of going into a ranked match or something you could choose from a list of leagues that you'd like to be a part of. Whether it be based on region or a type of match. Of course I think there would have to be a system for making these tournaments to make sure people are serious when making them.
Add more statistics from the match you just played. Amount of AP gained, supers used, supers landed etc (this will let players see where they need improvement)
The story mode could seem a bit more complete. I'm not even sure where or how all the characters met. But ultimately it's not a concern of mine as I think the gameplay is fantastic.
Maybe allow people to talk with each other after a match, and letting players know when other players have left.
Not so much about the game but, allowing for video capture on the vita so that we can share our greatest victories and funniest moments. Also it'll make it easier to share the game with a lot of people, driving up sales of both PSABR and the Vita in my opinion. (Almost spelt slaves instead of sales. I think I understand why this game is so addictive now) I bought the Vita specifically because of this game so I can play it whenever I wanted and would like a way to capture video for it even if I have to hook it up to a PC or Mac, this is the only version and device I can play it on.
And finally. Keep doing everything right.
Also I don't like the word perfect. It means the same thing as nothing, it just doesn't exist and if it did it would be incredibly boring, I don't see why people keep reaching for it.