Some zombies are pretty tough, plus, Flag Mummy Zombie can heal them. Strong attack plants are required to win this level.
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.
The strongest attack plants should be dragged onto the lawn. Ice plants as Snow Pea can be used to freeze enemies. Use defensive plants, such as Wall-nut, to protect other plants. You can also use other players' plants for stronger attack power and defense.