The planter is in the fourth tier of the workbench, and so the tier 4 workbench upgrade is required for this achievement. You only need to have five planters in your shelter for this achievement, they do not need to be in use, so seeds are not required. The materials you will need are:
1. 15x Buckets
2. 25x Wood
3. 15x Bulbs
Once you have the required materials, simply build five planters in your shelter, and the achievement should unlock. If you do not have it already, and you have 1 or more Seeds in your shelter inventory, you can interact with one of the planters and grow a plant, then later harvest it to win the 'Green Fingers' achievement.