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