Below is the complete list of all 39 trophies for Nex Machina. I doubt I will be able to unlock the platinum trophy for this game, but I'll try to get as many of them as I can and elaborate on each one as I unlock them.
Trophy Name: Nex Platinum
Trophy Type: Platinum
Description: Complete all trophies.
Trophy Name: Timber!
Trophy Type: Bronze
Description: Complete Techno Forest in arcade mode on any difficulty.
Trophy Name: I was frozen today
Trophy Type: Bronze
Description: Complete Crystal Mountain in arcade mode on any difficulty.
Trophy Name: Burnt offerings
Trophy Type: Bronze
Description: Complete Fire Caverns in arcade mode on any difficulty.
Trophy Name: Conquering dystopia
Trophy Type: Bronze
Description: Complete Machine City in arcade mode on any difficulty.
Trophy Name: Utterly experimental
Trophy Type: Bronze
Description: Complete Future Labs in arcade mode on any difficulty.
Trophy Name: The Orbital Throne
Trophy Type: Bronze
Description: Complete Space Station in arcade mode on any difficulty.
Trophy Name: Rookie
Trophy Type: Bronze
Description: Complete Arcade mode on Rookie difficulty.
Trophy Name: Experienced
Trophy Type: Bronze
Description: Complete Arcade mode on Experienced difficulty.
Trophy Name: Veteran
Trophy Type: Silver
Description: Complete Arcade mode on Veteran difficulty.
Trophy Name: Master
Trophy Type: Silver
Description: Complete Techno Forest on Master difficulty.
Trophy Name: 1CC
Trophy Type: Gold
Description: Complete Arcade mode on Experienced difficulty without continuing.
Trophy Name: It's a secret to everyone
Trophy Type: Bronze
Description: Discover a secret level.
Trophy Name: Someone must construct additional beacons
Trophy Type: Bronze
Description: Destroy every Secret Beacon in a single world.
Trophy Name: I'm prioritizing!
Trophy Type: Silver
Description: Defeat the Beamtron on Experienced difficulty with one or more enemies still alive.
Trophy Name: Dank beams
Trophy Type: Bronze
Description: Dash through 3 beams with single dash.
Trophy Name: *SLAP*
Trophy Type: Silver
Description: Deal a killing blow to a boss with a Sword attack.
Trophy Name: Look mom!
Trophy Type: Silver
Description: Finish a level without firing your primary or your secondary weapon.
Trophy Name: No hands!
Trophy Type: Silver
Description: Finish 5 levels in a row without movement, dashing allowed.
Trophy Name: I'm special, you're special!
Trophy Type: Bronze
Description: Save all Secret Humans in a single world on Experienced difficulty or higher.
Trophy Name: Last line of defense
Trophy Type: Silver
Description: Save all Humans and Secret Humans in a single world on Veteran difficulty.
Trophy Name: Doing it
Trophy Type: Bronze
Description: Succeed in 10 end-level minigames in a row on any difficulty.
Trophy Name: Because I can
Trophy Type: Bronze
Description: Clear a single world while succeeding in every end-level minigame on any difficulty.
Trophy Name: Not in my house
Trophy Type: Bronze
Description: Save a human while it's being harvested.
Trophy Name: Look at me go
Trophy Type: Bronze
Description: Complete a feat.
Trophy Name: Getting there
Trophy Type: Silver
Description: Complete 50 feats
Trophy Name: Fea(s)ts!
Trophy Type: Gold
Description: Complete 100 feats.
Trophy Name: 2+2=/=5
Trophy Type: Bronze
Description: Reach a human combo of 5.
Trophy Name: '-10+9*8-7*6+5*4+3^2+1 = 50'
Trophy Type: Silver
Description: Reach a human combo of 50.
Trophy Name: Nihilist
Trophy Type: Bronze
Description: Complete a single world on Experienced difficulty without saving any humans.
Trophy Name: Storm Runner
Trophy Type: Gold
Description: Beat Machine City on Experienced difficulty in under 5:45.
Trophy Name: No touching
Trophy Type: Gold
Description: Clear a single world on Experienced difficulty or higher without getting hit.
Trophy Name: Multiplierist
Trophy Type: Bronze
Description: Reach a multiplier of 50.
Trophy Name: Bronze challenger
Trophy Type: Bronze
Description: Earn 3 bronze medals in the Arena.
Trophy Name: Silver challenger
Trophy Type: Bronze
Description: Earn 6 silver medals in the Arena.
Trophy Name: Gold challenger
Trophy Type: Silver
Description: Earn 9 gold medals in the Arena.
Trophy Name: Behold, for he goes up to eleven
Trophy Type: Bronze
Description: Fully power up the Hero.
Trophy Name: Why are you running?!
Trophy Type: Bronze
Description: Kill a Disruptor.
Trophy Name: They died for a cause
Trophy Type: Silver
Description: Kill every Disruptor in a single world.