Here is the full list of all 30 Assault Android Cactus trophies - there are 12 bronze, 11 silver, 6 gold and 1 platinum.
Unlock all trophies
Earn an S+ ranking on all campaign levels
Reach a chain of 1000
Complete Boss Rush mode
Rescue the Genki Star
Lead the laser turret to defeat Medulla
Collect every Battery dropped in the Showdown level
Reach layer 25 in Infinity Drive mode
Reach Layer 15 in Infinity Drive mode
Unlock all items in the Art Gallery
Unlock all items in EX Options
Defeat one of Embryo's phases before he can relocate
Play as 8 Androids
Drop a cannonball down the hole in Filament
Destroy 3 enemies by driving another enemy through them with the Giga Drill
Destroy an enemy with Helo while it's caught by a Singularity
Finish any level without taking damage
Unlock all items in the Codex
Activate an EX Option
Unlock any item that costs credits
Earn an S+ rank on any level
Defeat Superstructure Engineer Venom
Destroy 15,000 homicidal robots
Destroy seven enemies with a single Rail Gun shot
Defeat Security Administrator Justice
Destroy every laser fence In Justice's first phase
Defeat Hydroponics Controller Vespula
Cause 3 mines to explode in succession without being shot
Reach a chain of 100
Defeat Production Overlord Embryo