I'm going to arbitrarily rule that it is impossible to keep your enemies alive long enough in the first battle for you to raise your JP to inordinately high levels. Thus, if done correctly (and with some luck as far as beginning stats and abilities), it would require:

1 Opening battle
1 as Squire
1 as Knight
1 as Monk
1 as Geomancer
1 as Archer
1 as Thief
1 as Lancer
1 as Chemist
1 as Wizard
1 as Priest
1 as Time Mage
1 as Oracle
1 as Summoner
1 as Mediator

So 15 battles.

Alternately you might rule that you really can't start power leveling until after the first three battles because of the guests, so you could say 17 battles.