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