First you have to heal the whole village (4 areas: The Entrance, The Square, The Fields and The Beach) from all infections so you get all the colors for your tool. You can check your progress in the menu screen's Village tab. Then you have to spray 10 beds of flowers with all colors each. You can change color in the menu screen's upgrades tab pressing the left or right trigger and pressing Y to select given color.
Beds of flowers are all the areas you healed from infected grass before. When you spray them with a new color the flowers in it will pulsate white until you finished the whole flowerbed then they turn to the selected color.
You need 10 red, 10 blue, 10 purple, 10 yellows (but you will get that playing the game) and maybe 10 rainbow ones. At this point I am not sure if it is possible do all all colors with the rainbow ones. I started out doing this by making around 10 rainbow flower beds. The achievement popped when I did 10 red and blue ones and interestingly 3 purple ones. So I might have miscounted the rainbow ones and they count as all of the colors. None the less it is a pretty easy achievement if you going to 100%. If not it is a late game thing with lot of grind.