Alright, I'm gonna give you guys a secret as to how a retired veteran of Injustice like myself beat 16Bit a match at evo in the Catwoman MU, which I have very little knowledge in.
Play footsies, and abuse d1 in staff to bait attacks.
If you can play decent footsies, you will probably do alright in this MU in neutral. Don't over texted yourself trying to pressure her up close with stand 1 stuff, Catwoman can beat it in a couple ways, and smart people don't give a shit about your stand 1. As soon as they see you doing d1 d1 d1 they are probably going to just mash d1 anyway because the risk/reward isn't very scary for them. Instead walk back and whiff punish their d1 with stand 1 or use neutral j1 at a range that will punish whiffed d1.
Second thing is using staff d1 to bait stuff. At far range, the threat of pound is sometimes more important than ground pound. Whiff d1 so they think you are doing ground blast, and depending on the range do different options. From full screen, do d1 and then be ready to mb b3 cat dash on reaction. From mid screen, use j2 to air to air them jumping over the fake ground blast.
The final thing I did is something to help make up for escrima's weakness in this MU. When you see her jump while in escrima, don't block it, instead dash under it. Forward dashing her j2 on reaction means you are the one who gets pressure after making it whiff and you can safely transition to staff. The only way for Catwoman to beat this is to switch to j3 instead.