Here is the full list of all 29 Assault Android Cactus achievements.
Rescue the Genki Star
Earn an S+ rank on any level
Destroy 3 enemies by driving another enemy through them with the Giga Drill
Activate an EX Option
Defeat Superstructure Engineer Venom
Destroy seven enemies with a single Rail Gun shot
Defeat Security Administrator Justice
Destroy every laser fence In Justice's first phase
Unlock any item that costs credits
Cause 3 mines to explode in succession without being shot
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
Destroy 15,000 homicidal robots
Defeat one of Embryo's phases before he can relocate
Collect every Battery dropped in the Collider level
Reach a chain of 1000
Reach Layer 15 in Infinity Drive mode
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
Drop a cannonball down the hole in Filament
Play as 8 Androids
Unlock all items in the Art Gallery
Unlock all items in the Codex
Unlock all items in EX Options