Here is the full list of all 9 Sproots achievements.
Hatch a new Sproot
Let a Sproot get a golden skill
Have 5 Sproots or more at the same time
Let a 50+ year old Sproot teach a young Sproot (< 10 years old)
Have a Sproot pass away from old age
Cook ratatouille, a smoothie, a salad or steak with fries in a geyser
Find a ruined village
Reach the 1000th cycle
Have a Sproot know at least 8 different crating recipes