The final dungeon of Final Fantasy IV: The After Years is essentially a boss marathon spanning over thirty floors. The best thing to do is to use a core team of five or so characters because you will not be required to use all of your characters at any given time. There are a few boss battles where you will get something special if you use a certain character, such as the boss battle with Rubicante, but these are few and far in between. Consult a guide to see if your team contains these necessary characters and you will likely never have to use any of your other characters again for any reason.