Here is the full list of all 27 Synthetik achievements.
Beat 5 rooms in Loop
Get a "SSS" Rating after a run
Survive the Armageddon Chamber on at least 200%
Gain over 500 HP from a heart core
Reach Credit limit 10000
Have 3 Shield Boosting Buffs active at the same time
Find a weapon in the super rare Divine variant
Open a timed chest in the last second
Defeat the Unstable Mass
Defeat the APC
Get a "S" Rating after a run
Hack the Server
Prestige at least once
Unlock all Research options
Reach level 25 with one Guardian Class
Reach level 25 with one Rogue Class
Reach level 25 with one Commando Class
Reach level 25 with one Specialist Class
Reach 25 with any class
Survive the Armageddon Chamber
Defeat the Last Defender
Obtain an artefact
Defeat the Arena Masters
Defeat Raptor Type E
Get a rare Ultra variant for a weapon
Defeat Experiment 57
Fail a timed chest with little time remaining