Here is the full list of all 64 Earth Defense Force 2017 Portable trophies - there are 60 bronze, 2 silver, 1 gold and 1 platinum.
Obtained all trophies
Healed a player with a Reverser weapon in co-op play
Destroyed 10 motherships
Destroyed 7000 gunships
Destroyed 600 new fighter craft
Defeated 50 giant spiders
Defeated a total of 40 Vallaks or Cyborg Vallaks
Destroyed 250 carriers
Obtained all available weapons
Cleared all stages on Inferno difficulty with Pale Wing
Cleared all stages on Hardest difficulty with Pale Wing
Chatted 10 times with another player in a co-op room
Defeated 500 enemies with a bike
Defeated 50 enemies with a bike
Defeated 2000 enemies with a tank
Defeated 2000 enemies with a Vegalta
Defeated 1000 enemies with a helicopter
Defeated 100 enemies with a helicopter
Cleared all stages on Hard difficulty with Pale Wing
Defeated 6000 spider-type bugs
Cleared all stages on Normal difficulty with Pale Wing
Pale Wing's health at 2000
Cleared all stages on Inferno difficulty with Storm
Chatted 10 times with another player in a co-op mission
Destroyed 100 Red Gunships
Destroyed 10 four-legged walking fortresses
Defeated 50 queens
Reinforced 100 other players with tempshields
Cleared all stages on Easy difficulty with Pale Wing
Destroyed 400 Hectors
Obtained 75% of all available weapons
Pale Wing's health at 1000
Cleared all stages on Hard difficulty with Storm
Cleared all stages on Hardest difficulty with Storm
Rescued 40 other players in co-op play
Obtained 50% of all available weapons
Destroyed 50 miniature Walking Arms
Defeated 10000 ant-type bugs
Cleared all stages on Normal difficulty with Storm
Storm's health at 4000
Defeated 200 enemies with a tank
Reinforced 10 other players with tempshields
Storm's health at 2000
Defeated 200 enemies with a Vegalta
Destroyed 700 gunships
Cleared all stages on Easy difficulty with Storm
Destroyed 1 mothership
Defeated a total of 4 Vallaks or Cyborg Vallaks
Destroyed 10 Red Gunships
Destroyed 60 new fighter craft
Defeated 5 queens
Defeated 5 giant spiders
Defeated 600 spider-type bugs
Destroyed 25 carriers
Obtained 25% of all available weapons
Rescued 5 other players in co-op play
Destroyed 1 four-legged walking fortress
Destroyed 5 miniature Walking Arms
Scored 15 weapon items in a single mission
Defeated 1000 ant-type bugs
Commanded a total of 60 allies
Destroyed 40 Hectors
Obtained 10% of all available weapons
Commanded a total of 10 allies