Whatever you do, don't change your combos for online. That shit messes with your head.
Personally, I've found most of Batgirl's combos to be pretty easy online, but I guess that's because I'm used to Black Adam. You just have to pay extra attention during her corner juggles to adjust if they get too low. For midscreen, you don't really need any fancy combos besides launch > bola > vortex.
The most annoying things online, as mentioned, is how strict it seems the timing is for punishes, anti-airs, and poking out of pressure. Batgirl doesn't have a big move that she can just spam when she's in trouble. Also, I like to use hard knockdowns and meaty B1/B2 a lot, and those are pretty hard to hit correctly online too, especially when you're going for MB option selects.