Here is the full list of all 43 The Solus Project trophies - there are 27 bronze, 13 silver, 2 gold and 1 platinum.
You collected all the trophies!
Collect all secrets
Collect 75 secrets
Carry 10 pieces of Tower Pieces in your inventory
Have 16 rocks in inventory
Drink champagne 3 times
Find Milson
Phone home
Complete the library
Fall for at least 5 seconds to your death
Collect 50 secrets
Explore the backside of the first island
Return to the Crossroad Island with an energy source
Find the energy source
Only eat alien 10 times in a row
Jump into the Hotspot crater
Reach the island of Hotspot
Enter the massive ice cavern
Enter the Ice Path
Complete Highpoint
Reach the island of Highpoint
Show some love to rocks - smash 20 rocks together
Blow up a torch in H2S without getting killed
Open 50 boxes
Find and pick up the music player
Get hit by lightning while holding a hammer
Return to the first caves after Flashpoint
Complete Flashpoint
Swim far off shore
Reach the island of Flashpoint
Dip your head in acid water
Have seen the dolls that cannot be unseen
Overcome the dark encounter
Extinguish a torch in water
Teleport 10 times in 30 seconds
Start the Communication Tower
Survive a tornado
Get hit by a spike plant
Find the ladder down
Collect your first secret
Complete your survival training
Hasn't picked up PDA until 5 minutes has passed
Set foot on the planet