Here is the full list of all 21 Syndrome achievements.
Complete the game
Read all logs
Defeat the Beast
Deactivate the ship's firewall
Access deck 8
Access deck 7
Pick up Cannon
Access deck 1
Cure 500 Hp of damage
Access deck 2
Got the Valkenburg running again
Have a droid working for you
Pick up SMG
Survived a trap
Access deck 3
Pick up pistol
Access deck 6
Pick up hacking device
Pick up tool
Access deck 4
Access deck 5