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