Grow your plants as normal and wait for them to FLOWER, not MATURE (where the achievements pop up that a flower has matured). You can tell if a plant has flowered if they grow a noticeable "flower" part out of them. You might have to zoom in the plant to be sure if it grows a flower, as some flowers are very small on some plants.

Select the plant that is flowered, then throw away the plant.

Your first achievement should unlock if you wait for it to flower. It approximately takes 25-30 days for a plant to grow and flower, depending on how you take care of the plant (i.e. not overwatering it, not let it get too thirsty, checking it daily, etc).

If throwing away 10 or above, it's recommended to wait for ALL OF YOUR PLANTS be flowered at the same time, so wait a few days for all plants to catch up to the ones that flower.

It's recommended to start counting after throwing away 10 mature plants.

Taken from here from Shrodu: https://astats.astats.nl/astats/Steam_Achievement_Info.php?AchievementID=47&AppID=375950#tabs-2

Quote:
"Before anyone reports this as being "not allowed", it has been deemed to be allowed by the devs and the mods/admins from the forum when I stated my case on these "Throw away" achievements. Here's what you gotta do:

1) Grow your 10 default plants legitimately.
2) Go into your Local Files for the Viridi game.
3) Create a spare folder and put a copy of EVERY .dat FILE INTO IT.
4) Turn off the Steam cloud.
5) Boot up your Viridi game.
6) "Throw away" your 10 mature plants. (That little button in the game with a tiny flower and a curved arrow by it)
7) Turn off your game.
8) Delete all your original .dat files. (Devs say to do this to get a new pot anyway. These .dat files you're deleting essentially say "This is a pot with no plants in it")
9) Copy your copy .dat files and put them back into their original places (This will have your 10 plants
appear again as if nothing ever happened)
10) Repeat steps 5-9 until you get the achievement.

This is not like "Advancing your clock". Technically you DID grow these plants, so this is allowed. All you're doing is recycling a copy of .dat files you created legitimately."

Shrodu - for alternative method mentioned in Astats
Proudlarry - For referral of method.