I gotta check you guys out! Wait, the parry works against normals?
He sort of has two "parries" and since both actually work against normals, I'll just explain the differences.
His Character Trait, the robot bats, can be used as a projectile or as a counter. During the counter they spin around him really quickly and if the opponent touches Batman they get popped up for a combo. The projectiles can be used to make yourself safe, to extend combos, or simply to zone.
He also has Cape Parry in which he drapes his cape across his body and if you attack him with a normal (I haven't seen it used against a projectile in gameplay footage, only normals), he does somewhat of a martial arts takedown (sort of like Arkham Asylum/City Takedowns). This leaves the opponent at Batman's feet.
I saw a couple vids of it being used, I'll see if I can find one of them to post here.
Edit: Found it. Go to 2:28
So in this vid, around 2:28, we see Batman keep using the Cape Parry at the end of the vid to close out the match. He finally lands it and we get to see the resulting takedown. We still don't know what EX does (grants a combo? works on projectiles?) or whether this works on all normals, but it looks like yet another solid tool that could set up for a nasty vortex. Once again, people are going to have to respect Batman far too much in this game haha.