The “Green Thumb” achievement requires players to grow aloe, blueberries, and coneflower in The Forest. Note that while the achievement’s description indicates “all plant types”, “Green Thumb” only requires the three mentioned plants.
Growing aloe, blueberries, and coneflower will require players to build a small garden and/or wall planters. Building a garden or wall planter is easy. Finding the plant types is also easy since they grow everywhere on the peninsula.
However, note that the player must acquire seeds and not just the plant. Therefore, players must acquire aloe seeds, blueberry seeds, and coneflower seeds.
Simply plant the seeds in the small garden or wall planters. Growing plants in the game do not require any other actions, such as watering. Players must simply wait a couple of days for the plants to mature.
The achievement should pop once all plants mature.