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