Here is the full list of all 63 Earth Defense Force 2: Invaders from Planet Space trophies - there are 58 bronze, 3 silver, 1 gold and 1 platinum.
Take down 100 Ace Fighters.
Take down 20 Mega Bombers.
Defeat 50 Queens.
Destroy 300 Darogas.
Obtain 50% of all available weapons.
Clear all missions on Normal as a Pale Wing.
Defeat 30 Bau Lords.
Reach 1000 armor as a Pale Wing.
Defeat 10000 giant insects.
Defeat 1500 mutated insects.
Defeat 6000 Baus.
Clear all missions on Normal an Infantryman.
Reach 2000 armor as an Infantryman.
Take down 250 Bombers.
Destroy 100 Deroys.
Clear all missions on Easy as a Pale Wing.
Take down 200 Shield Bearers.
Defeat 200 enemies with tanks.
Defeat 50 enemies with bikes.
Acquire 15 weapon boxes in a single mission.
Acquire 30 armor boxes in a single mission.
Clear all missions on Easy as an Infantryman.
Obtain 25% of all available weapons.
Destroy 30 Insect Hills.
Destroy Gilio and Giliora 180 times in total.
Defeat 100 Dragon Centipedes.
Obtain 10% of all available weapons.
Obtain 5% of all available weapons.
Obtain all other trophies.
Clear all missions on Hard as an Infantryman.
Clear all missions on Hardest as an Infantryman.
Clear all missions on Inferno as an Infantryman.
Clear all missions on Hard as a Pale Wing.
Clear all missions on Hardest as a Pale Wing.
Clear all missions on Inferno as a Pale Wing.
Clear all missions on Easy as an Air Raider.
Clear all missions on Normal as an Air Raider.
Clear all missions on Hard as an Air Raider.
Clear all missions on Hardest as an Air Raider.
Clear all missions on Inferno as an Air Raider.
In Co-op mode, rescue other players 5 times.
In Co-op mode, rescue other players 50 times.
In Co-op mode, rescue other players 120 times.
Take down 7000 UFOs.
Take down 250 Carriers.
Defeat Solas and Cyborg Solas 40 times in total.
Take down 9 Motherships.
Take down 4000 Imperial Guard.
Defeat 9 Solas Kings.
Take down 9 Adans.
Obtain 75% of all available weapons.
Obtain 100% of all available weapons.
Reach 4000 armor as an Infantrymen.
Reach 2000 armor as a Pale Wing.
Reach 2000 armor as an Air Raider.
Reach 4000 armor as an Air Raider.
Defeat 1000 enemies with tanks.
Defeat 100 enemies with helicopters.
Defeat 500 enemies with helicopters.
Defeat 250 enemies with bikes.
Heal another player with a Reverser-type weapon in Co-op mode.
Send 10 chat messages to another player during mission in Co-op mode.
Send 10 chat messages to another player in the room in Co-op mode.