Here is the full list of all 30 Planetbase achievements.
Build a base with at least 250 colonists in less that 60 days
Build a base with at least 100 colonists in less that 30 days
Build monoliths on all planets
Complete all milestones on all planets
Build a base with at least 100 colonists on the moon planet
Land on the gas giant moon
Build a base with at least 350 colonists
Complete tutorial
Have at least 20 armed Guards in your base at any given time
Have 5 operational Telescopes at any given time
Have 3 operational lasers, telescopes and telescope consoles at any given time
Build a base with at least 100 colonists on the frozen planet
Build all massive structures
Land on the frozen planet
Build a base with at least 100 colonists on the desert planet
Build a base with at least 100 colonists and 95% welfare ratio
Build a base with at least 100 colonists, with at least 25% of Bots
Build a GM tomato and GM onion pad
Fill a Massive Storage to more than 90%
Have at least 6 Driller Bots and 2 operational Mines at any given time
Have at least 1000 Coins in your base at any given time
Have at least 20 Vegetable boxes in your base at any given time
Build two structures and connect them
Land on the desert planet