You can get this achievement early on in the game. You will have a tutorial quest which wants you to create a planter box and plant some seeds. Once you've planted 20 berry bushes, you will unlock the achievement. The bushes do not need to have berries harvested to count (albeit harvesting them to turn them back into seeds is ideal).
Planter box materials:
8 x Dirt
My planter box glitched out on me while I was chopping down the berry bushes. If this happens, you will simply need to press
+
on the scarecrow to pick up the planter box, and place it back down. This will allow you to plant things again. Note: this may have been patched since I had recorded this video.
You'll need to complete this within the Spring and/or Summer seasons, as berries will not be able to be grown during Winter and Autumn, unless you use a Greenhouse (an unlock-able blueprint from the survival panel, though the materials to craft it makes it less desirable)
Please see the below video on how to unlock this achievement: