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