Here is the full list of all 14 Super Destronaut DX (EU) trophies - there are 2 silver, 11 gold and 1 platinum.
Get all the trophies
Complete 12 challenges
Reach to 100K points in Classic Mode
Reach to 50K points in Classic Mode
Complete 6 challenges
Reach 10K in Time Attack Mode
Reach to 25K points in Classic Mode
Complete 3 challenges
Complete 1 challenge
Kill 1 special red enemy
Hit one of the grey enemies
Reach 1K in Hardcore Mode
Die once
Kill 1 enemy