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