Here is the full list of all 9 Gunducky Industries trophies - there are 6 bronze, 1 silver and 2 gold.
Clear first level without taking any hits
Clear second level without taking any damage
Clear third level without taking any damage
Clear fourth level without taking any damage
Clear fifth level without taking any damage
Clear sixth level without taking any damage
Clear seventh level without taking any damage
Clear final boss without taking any damage
Beat the game