The first zombie that appears is a Cart-Head Zombie, so feel free to use a Shrinking Violet on it to weaken it. Plant a Bonk Choy on the row it comes from.
Rodeo Legend Zombie appears in huge amounts in this level. At the second flag triggering, there will be a group of five of them appearing in all rows (but thankfully there's only one per row). By that point, it is strongly recommended to have a column of Bonk Choys after column three (going left to right). Unfortunately, these plants will have to act as a cushion to them. However, use E.M.Peach right before they hit the second column of Bonk Choys to buy some time. If unsuccessful, your defenses will be wiped (at least, that's what happened to me). If successful, you should have a good amount of Bonk Choys remaining.
At one point, it might be possible for a horde of Prospector Zombies to jump into column 1 to eat your sunflowers (or whatever plants you have there). Hopefully you have shovel boost by now so you can recover some sun if they are threatened.
Going left to right, use Hurrikale to send all zombies back to column 8 if several get close to column 1. This level has no lawn mowers, so all zombies have to be defeated by whatever plants you have.
There are only two Plant Food given in this level, so use one of them on Shrinking Violet at the end of the level, and use the other one wisely if you must.
So long as you keep the pressure on the zombies, this level is beatable. If necessary, don't speed up time (the turbo button on the upper right).