I have a theory about all low tiers: They suck for a reason. There's always 1 or more fatal flaw in their metagame that makes them suck. For Zelda, the thing i find easiest to abuse is her shield. I think you need to become more fluid using fair-> grab. I saw you jabbing after the fair, and her grab is so slow it doesn't really matter. Also, you'd dsmash it, and it's like, solid enough for the dsmash to not connect. You threw turnips that she deflected, so you could start baiting or throwing them, then getting out of the bounceback trajectory. Also, be careful with your OoS game, because zelda can wait for you to think it's safe to do anything, then kick you. It's a good idea to let her land, but your nair oos can also stuff her pressure and counter and do other nifty nair oos things.
I know "make her suck" isn't the best advice, but the more you play her, the more her deficencies begin to become apparent. there's some other stuff but i'd have to rewatch the set ^_^;
Hope this helps