I get to fight one of the best zss players in the country very often, he's my brother.... so i know a lot about the matchup.
the best way to play this matchup is to be very aggressive. pressure her, she will lose in a fight with you up close. it's VERY easy to approach her if you can accurately power shield her forward b and d smash spam (which is not hard at all).
when you are right next to her just use your tilts wisely. d tilt messes her up a bit... try to get in a lot of grabs against her and use d throw.
you should never approach from across the screen with tornado, of course, that's not very smart do against any character, but she can punish it very well with her forward b or just hitting it with a charged d smash.
instead of using tornado on the ground, use the same strategy that you should be using against yoshi and olimar, which is tornadoing above her head. she can't stop it from there, there's nothing she can do if you use it correctly. so, just jump over her and tornado. keep in mind, she will be able to DI out fairly easily, but oyu won't get punished if you don't go too high with it.
don't fall for her charged d smash tricks that they go for while you land... that will rack up a ton of damage on you.
don't air dodge into her much, because her up tilt will catch you every time and put you in an unfavorable position. when she is below you, you're ****ed. her up air will beat everything you do... so don't try to challenge it with dair while you're above her. just try to go to the other side of her and fast fall your landing so you won't be juggled too much.
when she is charging d smash from across the screen, you can just glide attack her by going above the d smash, or just use the torando above her head, because although it does have a massive hitbox in the front of it, it does not have such an amazing upwards hit box.
when you're running at her and she's throwing out forward bs as her defense, running powershield and dash grab her. now the fight will be in your favor again. power shielding the forward b is very important (or just learning to shield it in general) because it is a very obvious move that can easily be shielded and punished for.
gimping her is very tough, you most likely won't get it off if you're new to the matchup... but work on nairing her out of her down b's invincibility when she uses it to get back on stage. start the nair about halfway through the invincibilty, it will outlast it and you can hit her before her down b attack or airdodge comes out.
once you've gotten rid of that, jut try to nair or dair her last jump away and grab the ledge.