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