Without Magnet-shroom, it will be difficult to get rid of both the toughest threats: Screen Door Zombies and Football Zombies (the latter being the stronger of the two), so you should be more careful around them. Fortunately, they don't show up much.
The sheer number of graves will spawn a huge number of zombies at the final wave, unless they are taken care of with Grave Buster.
Plant Sun-shrooms and Puff-shrooms for basic defense and sun gathering at the beginning of the level. Try to plant at least three columns of Puff-shrooms and two columns of Sun-shrooms if possible.
Plant Fume-shrooms and Wall-nuts whenever a Screen Door Zombie comes. Plant Repeaters when you see Football Zombies.
It is also important to keep in mind to not forget to use Hypno-shrooms just in case Football Zombies have consumed many of your plants. This is also a good way to use the hypnotized Football Zombies against other zombies as they are stronger and have high levels of toughness.
After your defense is more fully developed, plant Grave Busters on graves to get rid of them. Each grave eaten equals one more plant spot on your lawn and one less zombie spawner at the final wave.