I dunno just a couple opinions about Batman I've accrued over time during the era of the great batman army early in the game's life, hope there's something in there you haven't heard already. Anyone who disagrees is free to dissent with reasons. Question is a bit vague though, what offense in particular are you having problems with?
Bats have good hit advantage, so you have to respect that they can be released at any time. However there is no block advantage, so as soon as they come out you're free to press buttons, and that includes for the antiair. Imo the best option the best way is to pushblock, as it gets rid of bats, especially his jumping normals so you don't get wrecked by any bounce cancels. Sometimes clash is the best way to get rid of bats too. Obviously hitting him is a good way to get rid of them, but if only it were so easy lol.
He has no fast overhead, so if you mainly block low you'll take less free damage. This includes for the slide shenanigans. You can actually lab and see if your b3 is fast enough to punish the slide. If it is, then you are able to mb b3 and punish slide with no consequences as long as he has 1 or fewer bats out, which with his current state is more often than not.
f3 can cross over, especially in the corner. So if you lab it out with your character and see if it/when it does. As you know most f3 and b3 is very plus, and you of course can't bounce cancel off it, so another great time to pushblock.
B23 is a guaranteed punish for some characters. For instance Supergirl just needs to do instant u,d,4 and her laser beats him clean everytime. Looks like you play Firestorm, so perhaps instant air flame charge thing? I wish I could say I've labbed this one, but this is simple observation at the moment.
Special mention for 1,2 string. He's always doing it off a jumpin, so you can't exploit the high at the end. It's plus 4, and especially when bats are active it's scary to challenge him on that. This opens up his mind games for more block strings, grabs and even another jumpin if he thinks you respect him enough! Pushblock is a great option, but it's super risky if they have 2 bars and are crazy enough to bounce cancel on read against you. Everyone has different options against this mind game, so be sure to lab that one.