Here is the full list of all 30 Frozen Synapse Prime trophies - there are 16 bronze, 7 silver, 6 gold and 1 platinum.
Earn all of the other trophies
Win an Instant Skirmish match in 1 turn
Win your first Instant Skirmish match
Kill 100 enemy units in Multiplayer
Kill 50 enemy units in multiplayer
Play every game mode at least once
Kill 25 enemy units in Multiplayer
Have 3 or more enemy units visible in a match with visibilty set to 'Dark'
Win a multiplayer match without losing a single unit
Win a multiplayer match
Complete the campaign
Play the game at either 11:11 am or 11:11 pm
Make a kill with the Commando unit
Get 20 kills with the Grenade Launcher unit
Kill 3 enemy units with 1 explosion
Get 20 kills with the Sniper unit
Make a kill with the Devastator unit
In a match kill 3 enemy units with 1 Sniper unit
Get 20 kills with the Rocket Launcher unit
Get 20 kills with the Shotgun unit
In the Campaign extract all of the collectables in any Extraction mission
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
Get 20 kills with the Machine Gun unit
Complete Nashar: Extraction with both bodyguards alive
Complete the first Campaign mission.
Get a Gold rank on any Campaign mission
Get a Silver rank on any Campaign mission
Complete both Tutorials
Watch a Kill Cam replay