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