Here is the full list of all 16 Frozen Synapse achievements.
Complete the Single Player Campaign.
Get to level 100.
Get to Level 10.
Blow up the 4th wall in a level with a rocket launcher.
Lose a unit to a rocket.
Lose your first single-player mission.
Win a game of Charge.
Win a game of Hostage.
Win a game of Disputed.
Lose your first multiplayer game.
Win a game of Extermination.
Change the map generation settings.
Play an Instant Skirmish and win with only your machine gunner left alive.
Finish the tutorial.
Ignore an enemy.
Defeat 'Bin' in multiplayer.