Its name is a portmanteau of the compound "Carbon dioxide," and "garden," referring to the plants.
Blindly firing at the ground in the middle of a group of plants will likely get two or more vanquishes. However, if you aim for a specific plant in a group, that plant will get vanquished from the direct hit. The splash damage will likely vanquish one or more of the other plants, giving you a greater chance of earning the achievement. Remember that potted plants count too so going for a Sunflower with a Heal Flower is also a good tactic.
In Gardens & Graveyards, it is easier to get Garden Dioxide. When the plants are protecting the garden, jump to a rooftop and shoot a ZPG at the garden.