This should be the first achievement you unlock.
Start a new game by selecting Adventure Mode.
It costs 100 sun to plant a peashooter.
During level 1-1, you will be given your first peashooter. You should be able to plant two more peashooters during the first level. Therefore, you should have at least three for the achievement.
During level 1-2, you will be given two extra tracts of lawn. You should be able to plant at least seven peashooters during this level.
I recommend planting six sunflowers in the rear two rows of your lawn. Once you have 100 suns, plant a peashooter. The achievement should unlock during the final wave of zombies.