Batman ... is tricky if you are playing online don't even count it.
There are basically three types of batmen styles out there.
Run away and try to chip you to death with batarangs and bats.
Rush down behind flying bat trait.
Rush down without bat trait and use trait cancel to mixup b11 combo.
When I play batman I try to call 2 bats let the third charge so I can rush down behind 2 bats and have one for trait cancel. During charge time I am spamming batarangs running away. How fucking annoying does that sound?
At full screen you should be LGS spamming to chip him. If he begins to throw batarangs switch to MG because in a damage trade MG beats batarangs. This is the most favorable area for dstroke in this matchup. When you score a knock down you dont need to vortex or get in I think it's better to just back off and chip away imo.
If batman is rushing you down without trait you just need to zone correctly with dash mb F3, dash b1, dash b2 to kind of cut him off when he is in range. Mid range is still in your favor because SF will stop jump ins and MB F3 beat his options. Your dash combo starters have a high and low at hit one so you are still at an advantage midrange in my opinion.
His MB B3 is a good option but you can really just back jump your way out of it if you are at mid range.
Up close is the worst you just need to learn how to block then either mb F3 or back dash when his combos put himself at frame disadvantage.
The biggest problem is when batman sends his bat trait at mid range and dashes behind them. Or sends them on your wakeup. When you are blocked stunned by bats he will b11 or b23 you or crossup JF2 you.
If that's the case you can either block everything, you can jump over the bats with JF3 and hope he doesnt beat you in an air to air situation or D2 (in that situation you are aiming the J3 for the end of the dash so he cannot retaliate) or just ignore the bats and QS the dash because the QS trade with bats will be in your favor. If he blocks the QS he probably wont be able to complete the frame trap with the bats.
All those situations are very spacing specific.
If batman sends bats right in your face you just need to block or you're going to get blown up.
When I'm at mid range using batman im going to MB B3 without bats then use B2 or dash b113 with the frame advantage.
Or send two bats dash and do b23 or b113. As a mixup I can do b112 (the overhead) if I score a knockdown I can call bats and send on your wakeup or if you are used to blocking the 2 overhead ill b11 trait b11 again.
That's basically how you use Batman its just a variation of those two strings with trait cancels. 113 and 223 can be interupted by d1 between hits 2 and 3 so I never use them and neither would any other batman that knows what he is doing.
So basically to beat batman know the projectile trades that will win. Win mid range footsies by avoiding his B3 and smacking him with your dash mixups. And know your options against his bats and the typical b11 and b2 mixups.
None of this will help you online because lag makes reacting to all this shit impossible. If you play online use aquaman.