Here is the full list of all 14 Terra Lander trophies - there are 1 bronze, 1 silver, 11 gold and 1 platinum.
This is the platinum trophy and is unlocked automatically when all the trophies have been unlocked
Awarded for completing level 20
Awarded for completing level 18
Awarded for completing level 16
On any level with turrets complete the level without firing
Awarded for completing level 14
Awarded for completing level 12
Awarded for completing level 10
Awarded for completing level 8
Awarded for completing level 6
Awarded for completing level 4
Destroy all the turrets on any level
Awarded for completing level 2
Destroy all the fuel dumps on any level