Punish aggression with CDR Zyra
So I've discovered that Zyra has been a great champion for me vs assassins, Stomping Katarinas and Zeds pretty easily. and it comes from the Snare and the ability to poke them down without ever getting close.
Ignite isn't a good choice on her, I often take heal, ghost or barrier depending on the enemy. (barrier vs Zed) but playing a pushing lane that punishes them with thorn spitters works very well. also taking 2nd point in w then leveling q makes a huge difference, allowing you to ward your side bushes with plants while keeping them up to fight with.
This build however assumes you build CDR very quickly.
Doing this also makes her a phenomenal siege defender, able to protect towers from up to 3 opponents pretty easily.
This all being said, stealth and high wave clear are her downfalls. (she's better against aggressive enemies with low wave clear.)