Here is the full list of all 30 Frozen Synapse Prime achievements.
Complete the campaign
Make a kill with the Commando unit
Have 3 or more enemy units visible in a match with visibilty set to 'Dark'
Win an Instant Skirmish match in 1 turn
Get 20 kills with the Grenade Launcher unit
Play the game at either 11:11 am or 11:11 pm
Make a kill with the Devastator unit
Get 20 kills with the Sniper unit
Kill 3 enemy units with 1 explosion
Get 20 kills with the Rocket Launcher unit
Kill an enemy unit by bouncing a grenade off a wall
With 1 unit wipe out an entire enemy team of 4 or more units
In a match kill 3 enemy units with 1 Sniper unit
Get 20 kills with the Shotgun unit
Win your first Instant Skirmish match
In the Campaign extract all of the collectables in any Extraction mission
Get 20 kills with the Machine Gun unit
Complete Nashar: Extraction with both bodyguards alive
Complete the first Campaign mission.
Get a Silver rank on any Campaign mission
Get a Gold rank on any Campaign mission
Complete both Tutorials
Watch a Kill Cam replay
Earn all of the other Achievements
Win a multiplayer match
Win a multiplayer match without losing a single unit
Kill 25 enemy units in Multiplayer
Kill 50 enemy units in multiplayer
Kill 100 enemy units in Multiplayer
Play every game mode at least once