Here is the full list of all 54 Fate Tectonics achievements.
Survive placing Archaeomagosaurus
Reach level 2 in 3 minutes
Destroy the world once
Use every disaster power at least once in a single Doom event
Place a fleet in the smallest possible body of water
Construct fifty fleets
Place 30 ocean tiles in 30 seconds without a loss or mismatch
Settle one hundred cities
Construct twenty-five fleets
Throw away 100 tiles
Settle fifty cities
Reach Act 3
Place two world pillars next to each other
Create mountains by freezing a tsunami
Survive placing Auroara
Place two temples next to each other
Unlock all of Catlas' powers
Summon Catlas
Unlock all of Hogweed's powers
Unlock all of Barnacles' powers
Reach Act 2
Summon Hogweed
Place a tile that matches other tiles on all four sides
Construct five fleets
Summon Barnacles
Settle five cities
Unlock all of Penelope's powers
A city has grown into a castle
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
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 three times
Destroy the world five times
Destroy the world ten times
Survive an earthquake
100 mismatched tile placements
Replace a tile with a temple on it
Entire pantheon active