Complete the objective by using only your Hero Plant to kill the first zombies.
Try to place two columns of Sunflowers, one column of Peashooters, one column of Repeaters, one column of Snow Peas, and one column of Wall-nuts to defend all of the plants.
This will defend off all of the Buckethead Zombies.
If a zombie eats through all of your defenses, you have a Lawn Mower to kill all of the zombies in that row. Zombies will not spawn on that row for a while, so it will give you time to fix your defenses.