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