Plant two columns of Sunflowers and some Potato Mines at the start of the level. It is crucial to have two columns of Sunflowers as you need enough sun to last for three flags.
Plant as many Repeaters, Snow Peas, (and Threepeaters, if you have them) evenly on the lawn. You will need at least three columns to easily shield off Buckethead Zombies and Pole Vaulting Zombies.
Plant at least one column of Wall-nuts to defend your plants. Also, try to have some Squashes planted near the Wall-nuts to drag down a zombie or two. Replace them whenever possible.
On the final wave, four zombies will spawn from the pool (most likely two Conehead Zombies and two Buckethead Zombies). Let some Tangle Kelp pull down some of those zombies to save some bites off the Wall-nuts. From here, it should be really easy to pass the level with four lawn mowers remaining.