Here is the full list of all 52 Phoning Home achievements.
Find a safe passage through the desert
Find the Alien Graveyard
Defeat 10 Hostiles
Find and scan Tetrerium
Decrypt an alien text fragment
Defeat a Hostile
Craft 5 improvements
Find the alien junkyard
Discover ANI
Get to the top of the mushroom tree before entering the volcano
Overcome the Watchers
The night is dark and full of terrors
Discover planetary life
Defeat 50 Hostiles
Craft all available improvements for ION and ANI
Set foot into the Skyscraper
Explore an old cave
Find and decrypt all alien text fragments
Setup a Tumbler trap
Lure 10 Tumblers into traps
Fall into an abyss and survive
Complete the game without harming anything
Complete the game with ANI having a corrosion level between 20% an 50%
Complete the game with ANI having less than 20% corrosion
Complete the game with ANI having more than 50% corrosion
Find and scan all available Tetrerium
Discover the alien Mothership
Come to a final decision
I phoned home and all I got was this ...
Cherish life in all its shapes and forms
Rescue ANI from the beast
It's all snow and ice
Disover the failed expedition camp
Find and scan every single Seed available
Find a safe passage through dangerous waters
Reach the desert without healing once
Reach the glacier without healing once
Reach the volcano without healing once
Finish the game without healing once
Leave ANI behind when passing through a planet portal
Leave ANI behind 3 times when passing through a planet portal
Use every single portal inside the Volcano
Keep ANI under constant Coating in the desert
Keep ANI under constant Coating on the glacier
Keep ANI under constant Coating at the sea
Keep ANI under constant Coating in the volcano
Use less than 10 fuel through the whole game
Use less than 10 power cells through the whole game
Use the thruster 25 times
Use the thruster 250 times
Use the thruster 500 times
Climb all the way up the skyscraper