Here is the full list of all 20 Check Your 6 achievements.
Destroy an enemy aircraft
Win skirmish as Allies
Complete campaign as Allies
Win skirmish as Axis
Complete campaign as Axis
Destroy a surface target
Destory 20 enemy bombers
Destory 20 enemy fighters
Destroy 40 enemy aircrafts
Destroy enemy Ace aircraft
Win a scenario without loosing any aircraft
Win a scenario with only one aircraft left
Successfully drop 30 bombs
Destroy an aircraft with an anti-aircraft
Win a defend scenario without taking any damage to structure
Destroy an enemy aircraft by colliding with it
Destroy an enemy Ace with a green crew aircraft
Incinerate 3 enemy aircrafts in a single scenario
Win 20 scenarios as Axis
Win 20 scenarios as Allies