Here is the full list of all 56 Doomsday Vault achievements.
Coconut Palm saved
All Nutrients found
All Carbon Eaters activated
All Coconut Palm Crops grown
Banana saved
All Banana Crops grown
Cosmos saved
All Cosmos Crops grown
Neem saved
All Neem Crops grown
Maize saved
All Maize Crops grown
Cacao saved
All Cacao Crops grown
Calendula saved
All Calendula Crops grown
Yagua Palm saved
All Yagua Palm Crops grown
Apple saved
All Apple Crops grown
Kapok saved
All Kapok Crops grown
Papyrus saved
All Papyrus Crops grown
Date Palm saved
All Date Palm Crops grown
Lotus saved
All Lotus Crops grown
Sycamore Fig saved
All Sycamore Fig Crops grown