Here is the full list of all 15 Aerial Destruction achievements.
Destroy the enemy base in mission "Frontline Assault".
Have the helicopter shot down 10 times.
Complete all missions of the game.
Fire a total of 2000 rockets.
Protect the camp for few minutes in mission "Camp Defence".
Succesfully protect both temples in the "Ancient Ruins" mission.
Destroy the enemy troops and positions in the "Volcanic Island" mission.
Successfully support the allied retreating troops in mission "Convoy Support".
Destroy 500 armed pickups.
Destroy 100 buildings and fortifications.
Blast the bridge in mission "Bridge Destruction".
Destroy 300 tanks.
Kill 1000 mutants.
Buy 5 upgrades for the helicopters.
Defend the outpost in mision "Outpost Invasion".