You want to put your plants near the lawn mowers, and you want two full columns of sunflowers. Plant three sunflowers, then wait to see which lane the first zombie comes down. Plant a shooter that you can afford in THAT lane. Plant a sunflower, wait for a zombie, plant a shooter in the lane the zombie is using. Repeat. If there's already a shooter in the lane and the zombie doesn't have anything on its head, plant your shooter in a lane that doesn't have a shooter. Coneheads need 2 shooters in the lane usually. Bucket heads usually need 3.
I don't remember what you get on that level. If you have pole vaulters, plant the cheapest thing you have available right at their feet as they show up, so that they jump over it and slow down.