Here is the full list of all 43 The Solus Project achievements.
Carry 10 pieces of Tower Pieces in your inventory
Hasn't picked up PDA until 5 minutes has passed
Phone home
Read all stories
Return to the Crossroad Island with an energy source
Find the energy source
Jump into the Hotspot crater
Collect all secrets
Drink champagne 3 times
Reach the island of Hotspot
Enter the massive ice cavern
Enter the Ice Path
Return to the first caves after Flashpoint
Collect 75 secrets
Fall for at least 5 seconds to your death
Complete Highpoint
Reach the island of Highpoint
Blow up a torch in H2S without getting killed
Complete the library
Show some love to rocks - smash 20 rocks together
Have 16 rocks in inventory
Swim far off shore
Find Milson
Collect 50 secrets
Find and pick up the music player
Only eat alien food 10 times in a row
Get hit by lightning while holding a hammer
Complete Flashpoint
Open 50 boxes
Reach the island of Flashpoint
Teleport 10 times in 30 seconds
Dip your head in acid water
Have seen the dolls that cannot be unseen
Get hit by a spike plant
Overcome the dark encounter
Start the Communication Tower
Find the ladder down
Extinguish a torch in water
Explore the backside of the first island
Survive a tornado
Collect your first secret
Complete your survival training
Set foot on the planet