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