Well, we have to take into account, are we considering Bale's take on batman or are we still with clooney, or Val Kilmer, or Keaton, or are we looking at the comics.
I will discuss it from the aspect of the Dark Night and Batman Begins, because it is the same actor with the same take on the character, and that is what just came out.
Everyone would aree that Batman, and Bruce are both definitely Introverts.
His Intuition is clearly there, yet he is pretty damn observent of what is going on around him, so S and N in I am not sure on, but they would have to be secondary and tertiary well developed functions, because of how equal they are and how he uses both. Think of how he is always observing the enviornment for danger, yet is always scheming how to get advantage of the situation.
I don't know how to explain this in any way whatsoever, but Bale had Batman ride the F train the whole way through both movies. He seems so irrational in his choices, like deciding to kill his parents murderer at the beginning of the movie, and then just deciding to leave after he can't kill falcony. I personally would say Fi, more than anything on this guy, because he doesn't seem to get his moral compass from anyone, he just has it, and yet he really does really on it for his whims, a T doesn't just decide to hop on a ship and stowaway and other irrational actions on the feelings of a moment.
The P and J delimma, hmm... I am not sure, but does seem very organized, and does not like leaving things to chance and does get frustrated when his shit doesn't work to plan, like hmmm beating the shit out of joker in that one scene (I am not going to ruin the movie so I will shut up). J wins here.
He just doesn't seem like an IxFJ to me. I don't know...