Here is the full list of all 27 Bandit Six: Combined Arms (JP) trophies - there are 10 bronze, 10 silver, 6 gold and 1 platinum.
Be victorious and crush all the enemy forces
Upgrade any gun to inflict the maximun level of damage
Upgrade any gun to the maximum rate of fire
Upgrade any gun to the maximum cooling level
Buy 3 different power ups
Complete a mission with a rank of three stars outside of basic training
Complete all the timed missions
Get a kill of every type of enemy plane
Get maximum guns and armour
Get a kill streak of at least 5
Complete ten missions with a rank of three stars
Complete all the protection missions without losing a single bomber
Complete a mission with no damage
Complete all the missions with a rank of three stars
Upgrade all of your guns on one level
Destroy 15 enemies in a level with the machine gun
Shoot down a helicopter with the artillery
Complete a level using only the mortar and artillery
Get a rank of three stars outside of basic training
Complete a level without losing a single gun in a level after basic training
Sink an enemy destroyer
Destroy all the landing craft in a level before they deploy
Get all the generals to safety
Get a rank of three stars on 5 levels
Destroy all the transport helicopters in a level before they land
Shoot down 5 helicopters in one level with the mortar
Complete every level with a rank of three stars