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