I did the LoC Baal fight (real tyrant) and took me a while to sort things out in order to PPS from the majin. I killed him with the PPS, and it worked after ten tries of killing the majin. I actually stole a LoC Baal Axe from my tenth kill of the majin via PPS. So just to let you know, This works the same way as it was in the PS3 version onto this Vita version.
Oh by the way, LoC Baal has 1.2 billion hp+ so I would suggest using a person who has the best innate evility like Laharl, have him attack last using an S Rank Skill to kill at least 1 Baal. Rarity on the Baal Axe is always 0. I checked using a steal hand.
To unlock the Real Baal fight, you need to have all of the characters in the game in your party. Yes that means all the post game characters, vita content characters, and even the DLC characters that are all in the game.
Oh and yes you CAN re-battle Baal after defeating him.