ZSS OoS game is pretty bad and her grab is slow so just grab much as normal.
Alwaysbe aware of her little projectile thats how you get opened up most of the time. Try dealing with it without leaving yourself open (so powershield or jump over it, but if you shield normally or roll or spot dodge or try to clank thats what she waits for).
Note that even if looks like you could, you can't dodge under her neutral B. Sometimes countering is OK but be aware it leaves you open.
Mix up your DIs against her aerial combos becuase you need a freaking good reaction time to follow the DI, even with her amazing mobility
Do Marth stuff: Some fundamentals always work!
Approach: Don't dashdance as often as you would normally because of that projectile. Approaching is kind of hard just use your movement to avoid her neutral side B (full jumps and WDs mainly) and then a grab is your most reliable option, next are fair and nair (maybe something else I forgot).
The only thing you should deal with when pressuring is her frame 2 jab so be aware that if she is for example crouchcancelling that move will get you fast.
Edgeguarding aint easy... Well, f-throw-> dair works against bad di as surprise around 30%, probably even more.
Otherwise just grab the ledge, wait for her to do the Forced Double Jump and then up-air.
If you recover, try to be not in her D-smash range cause she can get a f-smash a bair or some 20XX nasty footstool setup out of it.
I hope that helps
