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