Here is the full list of all 51 Earth Defense Force: Insect Armageddon trophies - there are 37 bronze, 12 silver, 1 gold and 1 platinum.
Beat the game on Inferno Dante? Is that you?
Make it through 5 Survival Mode Waves in one session Five Alive
Kill 25000 Enemies Master killer
Beat the game on Hard Rule #3
Kill 10000 Ants Good start!
Kill 100 Small Hectors Hector Who?
Destroy 1000 Gunships 1000 down
Get 500 kills with Base Turrets Like a Turret in a punchbowl...
Destroy 100 Anthills/Spider Nests Hit'em where they live!
Get 500 kills with the Tank Tanks a lot
Kill 100 Wasps Get out of my yard!
Get 500 kills with the Mech It's a Mech-a-delic freakout!
Destroy 500 buildings Urban renewal, EDF style
Destroy 500 cars/vehicles Traffic un-jammer
Incapacitate a teammate Way to be!
Get 250 kills with the Lander Turret Hot LZ? What hot LZ?
Beat the game on Normal Easy Peasy
Kill 5000 enemies Bug juicer
Kill a Queen Ant The Queen is dead!
Kill 10 Mantises Preying ON Mantis
Destroy 10 Carriers Tora! Tora! Tora!
Kill 10 Wasps Empty nest
Kill 10 Bomber Spiders Drop the Bombers!
Destroy 100 Gunships Mmmmm...Gunships
Destroy 10 Anthills/Spider Nests Total Nest-ruction!
Kill 10 Small Hectors What's a Hector?
Kill a Large Hector The bigger they are...
Kill 100 Ticks Tick...Tick...
Kill a Mantis We mean it Man...
Kill 1000 Ants 1000? There must be a jillion of those things! Get busy!
Kill a Daddy Long Legs Well he's a long gone daddy...
Destroy 500 world objects You litterbug
Kill 100 Spiders You want a medal for that?
Unlock all Armors Sharp dressed man
Revive a teammate Good job! Now do it some more
Kill 100 Ants 100? That's nothing!
Earn all Trophies in the game Get a life
Kill 10000 Spiders Arachnocidal maniac!
Kill 5000 Ticks Boom!
Destroy 10000 Gunships Bet you died a lot doing this...
Survive 100 (total) waves in Survival mode Big Wave Rider
Destroy 100 Carriers Mayday! Mayday!
Collect All Dropped Weapons Look what the Hector Dropped!
Level up an armor completely Isn't that special...
Level up all armors completely Well, Hello, Mr. Fancypants!
Purchase all available weapons for a single armor You are a consumer
Purchase all weapons for all armors All gunned up!
Revive 250 teammates You're so nice
Survive 500 (total) waves in Survival mode I will survive!
Get 1000 kills in Survival mode Still on the island
Get 10000 kills in Survival mode They got...FRAGGED!