Here is the full list of all 39 Leave The Nest achievements.
Unlock Elly the energetic eagle
Unlock Cardy the charismatic cardinal
Collect 100 coins
Fly through 5 zones
Get a 15X multiplier
Unlock Spoopy the spooky bat
Unlock Touky the tough toucan
Unlock Corey the caw caw crazy crow
Collect 50 coins
Collect 10 coins
Fly with the train for 5 seconds
Dive for 2 seconds
Unlock Polly the pirate parrot
Get a 5X multiplier
Fly above the clouds for 8 seconds
Fly for a minute
Fly above the clouds for 5 seconds
Touch the sky
Fly above the clouds for 2 seconds
Fly through 50 windows
Fly through 10 windows
Fly through 25 windows
Fly for 5 minutes
Fly for 10 minutes
Get a 50X multiplier
Fly through 10 zones
Fly through 15 zones
Fly with the train for 10 seconds
Unlock Firdy the fast bird
Visit every zone in one flight
Unlock Philly the fastest falcon
Unlock Manny the mallard with valor
Unlock Finny the finch who doesn't flinch
Unlock Sally swan the swift skimmer
Unlock Henry the hyper hummingbird
Unlock Billy the bold bluejay
Unlock Gully the seagull with no equal
Unlock Olly the observant owl