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