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