The icon features a Peashooter, being crossed off by a "no" symbol.
Simply playing as a Zombie Hero should net you this eventually. Note that even if you lose the match, so long as you destroyed a plant, it will count.
Insta-kill tricks, such as Rolling Stone, Rocket Science, Cut Down to Size, and Locust Swarm, will do you plenty of good. Especially notable is Weed Spray, which is theoretically capable of destroying every plant on the field. Rustbolt is an optimal hero, since the only Insta-kill tricks he lack are Locust Swarm and B-flat.
In addition, Deadly zombies will be of extra use to you, as they will immediately destroy a plant regardless of its health upon attacking. Smelly Zombie is a cheap, effective zombie for this. Though Super Stench can also be useful, as it gives every zombie Deadly, it is restricted to only Super Brainz and Impfinity, so it's not always reliable.
- This is similar to the achievement, Back to the Grave!.