The zombies in this level were all unbelievably tough. Upgrading the plants was required to finish the 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.
Strongest attack plants should be dragged onto the lawn. Ice plants as Snow Pea can be used to freeze enemies. Defensive plants should be placed in front of the attack plants, especially the middle one, to prevent the boss and the zombies from killing your main attack. Healing plants should also be used to recover huge damages. Don't forget to use other players' plants.