Here is the full list of all 27 Super Destronaut DX: Intruders Edition trophies - there are 10 bronze, 9 silver, 7 gold and 1 platinum.
Get all the trophies
Reach 300K points in Tate Mode
Reach 200K points in Tate Mode
Reach 100K points in Tate Mode
Reach 10K points in Hardcode+
Reach 5K points in Hardcode+
Reach 3K points in Hardcode+
Reach 10K points in Hardcore Mode
Reach 1K points in Hardcore Mode
Reach 50K points in Time Attack Mode
Reach 10K points in Time Attack Mode
Reach 100K points in Classic Mode
Reach 50K points in Classic Mode
Reach 25K points in Classic Mode
Complete 30 challenges
Kill 50 special red enemies
Die once
Complete 20 challenges
Kill 25 special red enemies
Complete 12 challenges
Kill 10 special red enemies
Complete 6 challenges
Complete 3 challenges
Kill 1 special red enemy
Complete 1 challenge
Hit one of the grey enemies
Kill 1 enemy