Her plants are fairly easy to kill. Her seeds are largely limited and most of the ones she puts down are randomly generated. The longer she is in one place, the stronger she becomes, and you have to work around that. However, when she is on the move, she becomes much more vulnerable. If you can weather her storm, she goes down fast, and usually pretty hard.
A good Zyra player will punish you for your aggression and positioning mistakes. That's what she's designed to do. However, as a Zyra main, I can tell you outright that there are numerous ways to simply erase her even if she makes no mistakes. Miss Fortune is a great example of using her plants against her (See MF's Q). Morgana can eliminate plants with her W very quickly. Any gap-closing champion can really hurt her badly (Leona and Alistar come to mind, lets not mention Junglers). Exhaust nullifies everything she does and lasts for almost the entire duration of her awakened plants if put down at the same time, on top of making her squish even louder.
She is strong in the right hands and in the right circumstances, like many other champions. But she's far from over-powered and does fall off some as the game goes on.