Here is the full list of all 54 Fate Tectonics achievements.
Reach level 4 only using tile placement powers
Place 30 ocean tiles in 30 seconds without a loss or mismatch
Place two world pillars next to each other
100 mismatched tile placements
Place two temples next to each other
Have a castle within 2 minutes of starting a new age
Pestur is the only active Fate
Reach level 9 only using Penelope (and Pestur)
Reach level 7 without placing a fleet
Replace a tile with a temple on it
Destroy the world five times
Throw away 100 tiles
Reach Act 3
Create mountains by freezing a tsunami
Survive placing Auroara
Settle one hundred cities
Construct fifty fleets
Place a tile that matches other tiles on all four sides
Destroy the world three times
Use every disaster power at least once in a single Doom event
Unlock all of Catlas' powers
Settle fifty cities
Summon Catlas
Unlock all of Barnacles' powers
Construct twenty-five fleets
Reach Act 2
Unlock all of Hogweed's powers
Summon Hogweed
Destroy the world once
Place a fleet in the smallest possible body of water
Construct five fleets
Summon Barnacles
A city has grown into a castle
Unlock all of Penelope's powers
Settle five cities
Survive placing Archaeomagosaurus
Use a single tile to start a new unconnected landmass
Repair ten crystal pyramids
Reach level 7 without any Fates triggering a disaster
Reach level 4 without losing or replacing a tile
Reach level 7 without Pestur getting angry about anything
Have Penelope, Barnacles, Hogweed, Pestur and Catlas at 80% anger at the same time
Place 20 grassland tiles in 30 seconds without a loss or mismatch
Reach level 2 in 3 minutes
Collapse entire world with a single blight
Collapse entire world with a single earthquake
Collapse entire world with a single tsunami
Collapse entire world with a single blizzard
Collapse entire world with a single meteor shower
Collapse entire world only by placing industry
Collapse entire world with a single hole
Destroy the world ten times
Survive an earthquake
Entire pantheon active