Here is the full list of all 31 Graviteam Tactics: Operation Star achievements.
Eliminated 50 enemy soldiers
Eliminated 10 enemy soldiers with one squad or a vehicle
Got the highest award
Eliminated 100 enemy soldiers
Destroyed 10 enemy armored vehicles
Destroyed 25 enemy armored vehicles
Captured 10 enemy soldiers
Captured 20 enemy soldiers
Captured 3 vehicles
Captured 10 vehicles
Eliminated 20 enemy soldiers with one squad or a vehicle
Eliminated 50 enemy soldiers with one squad or a vehicle
Destroyed 3 armored vehicles with one squad or a vehicle
Destroyed 5 armored vehicles with one squad or a vehicle
Destroyed 2 armored vehicles with one infantry squad
Destroyed 4 armored vehicles with one infantry squad
Sent 2 airstrikes
Sent 3 airstrikes
Sent 3 artillery bombardments
One squad or a vehicle got 5 medals
One squad or a vehicle got 10 medals
Got 15 medals for one battle
Won a battle with one last soldier
Eliminated all enemy soldiers
Won a battle with no casualties
Won a battle with a kill ratio of 3 to 1 in player's favour.
Won a battle with a kill ratio of 5 to 1 in player's favour.
Captured all flags in a tactical battle
Destroyed all enemy force on operation level
Destroys the key enemy unit
Completed all tasks for operation