Batman is good, just make sure your defense is on point because you kan't D2 AA him after blocking a bat like some characters kan and Arrow's D2 is on the slower side. It all depends on how good your defense is. Otherwise it's probably a bad match up.
Aquaman used to be bad, and it still might be. You have to kommit to shooting arrows if you get lucky enough to get past the 23+ frame start up since FTD will katch you for good damage. The floaty jump Arrow has, along with his reliance on J3 (which is slower), makes it easy for Aquaman to AA, and then Aquaman has faster footsie normals. I think it went from terrible to bad, but I haven't played the new match up too much.
Wonder Woman is probably about even now. She kan check him and get a 50/50 off a jump in, which happens more often since Arrow needs to shoot arrows back to back more often to stop her shield toss. Pretty even or in Arrow's favor.
Cheetah is pretty even or in her favor. She kan jump over arrows pretty well so you have to bait it, then in the neutral, her D3 goes under Arrow's F2. I played against Xian a lot after Viennality. Arrow's slow D2 is again the weakness that limits Arrow. The problem is that she gets good jumps from anywhere on the screen and she kan bait the slow D2. I actually AA with standing 1 for some spacings or angles of her jump. She outdamages Arrow and has good mix ups.
Supergirl used to be an even match up but now it's just bad for Arrow. Supergirl kontrols the pace of the match and out damages arrow because you'll never get a 111 punish unless she plays really risky, which she doesn't need to. One good thing some people don't realize though, is that she kan't teleport on reaction to Arrow's regular shots. If she does, just hold forward and she eats a full 111 punish.
Catwoman is a pretty good match up for Arrow. It's either 5-5 or in his favor. Especially not that she lost her armor on her dash.
If you need help learning Arrow, just ask me anything about him.