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