Some zombies have high health, but can still be defeated easily if the plants are well-upgraded.
Upgrade your plants' level by playing previous levels. Then upgrade them more with Puzzle Pieces and the Oven in your house. Hunt more Puzzle Pieces from previous levels.
Strongest attack plants should be dragged onto the lawn. Ice plants as Snow Pea can be used to freeze enemies. Healing plants, like Twin Sunflower, defensive plants, like Wall-nut, or charge-attacking plants such as Iceberg Lettuce or Cherry Bomb, are optional.