I had a really long set with a pretty good Batman, I think the final score was 70-5 or something like that. It seemed like Batman has the advantage everywhere except up close. Although even up close it was not that advantageous for me.
At range he would throw Batarangs with his trait up. If I jumped he would let the trait go and follow with the MB zip for around 30-40%. If I crept up he would wait till I got close enough to use my jump, the F2,D/D1 mix-up, command grab, or a Double Punch, and hit his B2,3...which beat all those options I mentioned...or beat me air to air(only my J1 or preemptive JD3 had a chance to beat his JI2)...or cross me up with his JI2. It felt like Batman's B2,3 and JI2 covered all my options and made him completely safe. Oh, and using the charge had him using the trait with Batarangs to eat my armor and lead into combos, or he'd MB his Batarang to KD me and reset the space.
I tried using lvl 3 venom for a couple of matches to go invuln through the projectiles, but that was where he knew I would charge and just baited it for punishes...while waiting for it to run out and rush me down.
I saw my most success getting in range for a command grab or a B1,1,2. That said, he was not scared of the command grab at all, and would parry just about every time he woke up. One match I might have command grabbed him 4 times in a row on his wakeup.
One last thing. By him staying at full screen most of the match, and taking into account his movement speed vs mine, he was able to use and control all the interactables with spacing.
I tried to describe the matches as best I could without making this too long, but yeah...I was very lost.