Well Sinestro players don't give as much grief, you just gotta be grounded or as I do randomly take flight and drop quickly and be ready for some falling rocks and watch for wake-ups. Batgirl I think its just gonna be a matter of playing the patientce game and making sure to understand her mix-ups. One thing I have learned is that her D1 can give BG trouble.
You cant fly at all against a good Sinestro, unfly has recovery and Sinestro can use shackles and catch you when you're landing. Plus once his trait goes up its game over for HG, no movement allowed <__>
Batgirl is more of less the same thing, the teleport clips HG's wings as you cant jump or fly without getting snatched. she can just keep zoning you with bola and batarangs and building meter while you're slowly inching in then she can derp with her batwheel thats a 50/50 for whatever fuckin reason or use the evade~1 move to fly fullscreen away and do the same thing again.
Thats just the optimal way, upclose she can use b12 which has enough range to whiff punish our d1 and go into her vortex, plus anti-airing her with d2 is omega risky as she can teleport and snatch that..
Its just a "no fun allowed" matchup as batgirl's dirt is much better while HG's is all nullified, you're better off playing another character even if you're not that good with them as you actually have tools to use if you do that.
DS is fucked too coz air guns and pizza cutter do the same thing which is nullify most of our tools.
I've yet to fight a decent Cyborg so i cant comment on that MU.