Here is the full list of all 39 Nex Machina achievements.
Complete all achievements
Complete Arcade mode on Veteran difficulty
Complete Techno Forest on Master difficulty
Complete 100 feats
Earn 6 silver medals in the Arena
Earn 9 gold medals in the Arena
Clear a single world while succeeding in every end-level minigame on any difficulty
Complete a single world on Experienced difficulty without saving any humans
Earn 3 bronze medals in the Arena
Reach a multiplier of 50
Defeat the Beamtron on Experienced difficulty with one or more enemies still alive
Save all Humans and Secret Humans in a single world on Veteran difficulty
Reach a human combo of 50
Complete 50 feats
Beat Machine City on Experienced difficulty in under 5:45
Complete Arcade mode on Experienced difficulty without continuing
Clear a single world on Experienced difficulty or higher without getting hit
Finish a level without firing your primary or your secondary weapon
Finish 5 levels in a row without movement, dashing allowed
Complete Arcade mode on Rookie difficulty
Complete Arcade mode on Experienced difficulty
Succeed in 10 end-level minigames in a row on any difficulty
Complete Space Station in arcade mode on any difficulty
Deal a killing blow to a boss with a Sword attack
Complete Future Labs in arcade mode on any difficulty
Save all Secret Humans in a single world on Experienced difficulty or higher
Complete Machine City in arcade mode on any difficulty
Dash through 3 beams with single dash
Complete Fire Caverns in arcade mode on any difficulty
Complete Crystal Mountain in arcade mode on any difficulty
Destroy every Secret Beacon in a single world
Kill every Disruptor in a single world
Discover a secret level
Fully power up the Hero
Complete Techno Forest in arcade mode on any difficulty
Reach a human combo of 5
Complete a feat
Save a human while it's being harvested
Kill a Disruptor