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