Here is the full list of all 15 DOGOS trophies - there are 14 bronze and 1 gold.
ELIMINATE THE GOLIATH
ELIMINATE 10 ELITES UNITS
ELIMINATE 50 ZEETNUK EGGS
ELIMINATE THE ANNIHILATOR
ELIMINATE 100 TANKS
ELIMINATE 25 BOATS
SHOOT 100,000 ROUNDS
DESTROY 20 ZEETNUK STRUCTURES
ELIMINATE 200 AIR UNITS
ESCAPE FORM THE CAVERN
COMPLETE THE TRAINING LELVEL
GET ALL BADGES
COMPLETE ZEETNUK STATION: INTRUSION WITHOUT LOSING LIVES
COMPLETE THE OVERTRAIN MISSION WITHOUT LOSING LIVES
FINISH THE GAME IN THE HIGHEST DIFFICULTY SETTING