Here is the full list of all 47 Final Approach achievements.
Fail a mission by letting the timer run out
Land 100 Planes
Complete a mission with full Karma
Land 50 Planes
Land 25 Planes
Land 2 planes on 2 different runways at the same time
Put out 1 Plane Fire
Scare birds off 1 runway
Land 1 Helicopter
Land 1 Plane
Shoot down 100 Alien Ships
Collect all Story Mission Badges
Sort 100 pieces of Luggage
Successfully bomb 25 targets
Land 100 Private Planes
Land 100 Helicopters
Land 200 Helicopters in Metro City
Solve 20 Button Puzzles
Land 100 Commercial Planes
Capture 5 Criminals
Put out 100 Plane Fires
Crash 100 Planes
Put out 25 City Fires in Metro City
Shoot down 100 Alien Ships with machine guns
Land 200 Planes on Parrot Island
Land a Plane that is out of fuel
Complete a mission with less than 10% Karma remaining
Let 20 Planes run out of fuel
Drop a burning car in the rooftop pool in Metro City
Land 200 Planes at Metro Airport
Let 10 City Fires burn out of control and explode
Put out 50 Helicopter Fires
Land 100 Military Planes
Get 3 Stars on all missions
Shoot down 100 Enemies with Turrets
Land 500 Planes
Land 1000 Planes
Find a secret in the Hangar Office
Throw a party in the Hangar Office
Let the non-swimmers get eaten by sharks
Complete the Air Racer objective in Blue Skies in under 14.1 seconds
Complete the Air Racer objective in Blue Skies without crashing
Get 3 Stars on the Challenge Mission "UF-Oh No!"
Get 3 Stars on the Challenge Mission "Airport Overload"
Get 3 Stars on the Challenge Mission "Put a Ring On It"
Get 3 Stars on Halloween Challenge "Pumpkin Picking"
Get 3 Stars on Halloween Challenge "Trick or Treat"