Here is the full list of all 34 RESOGUN (PS3/Vita) trophies - there are 19 bronze, 9 silver, 5 gold and 1 platinum.
Reach the end-boss of any level using boost only
Kill 50 enemies with one boost
Complete the game with Phobos
Complete all levels on Rookie difficulty
Complete all levels
Complete Mefitis
Fully upgrade the ship
Fully upgrade the main gun
Complete Febris
Fully upgrade the overdrive
Get a multiplier of 5x
Complete Decima
Complete Ceres
Save a human from an Abductor's beam
Complete Acis
Throw a human to the escape pod
Save a human
Get all trophies
Complete all levels on Experienced difficulty
Complete all levels on Veteran difficulty
Save two humans within a span of one second
Kill 100 enemies during Overdrive
Complete a level on Master difficulty
Complete Arcade mode without losing all lives, on Experienced difficulty
Save all humans
Save all humans on Acis
Save all humans on Ceres
Save all humans on Decima
Save all humans on Febris
Save all humans on Mefitis
Get a multiplier of 10x
Get a multiplier of 15x
Complete the game with Ferox
Complete the game with Nemesis