Here is the full list of all 37 Leave the Nest trophies - there are 24 bronze, 8 silver, 4 gold and 1 platinum.
Unlock Touky the tough toucan
Unlock Corey the caw-caw-crazy crow
Unlock Philly the fastest falcon
Fly through 5 zones
Get a 15x Multiplier
Collect 50 coins
Collect 10 coins
Fly with the train for 10 seconds
Fly with the train for 5 seconds
Get a 5x Multiplier
Fly above the clouds for 8 seconds
Dive for 2 seconds
Fly for a minute
Unlock Polly the pirate parrot
Fly above the clouds for 5 seconds
Fly above the clouds for 2 seconds
Touch the sky
You collected everything for Leave The Nest
Fly through 10 windows
Fly through 25 windows
Fly through 50 windows
Fly for 5 minutes
Fly for 10 minutes
Collect 100 coins
Get a 50x multiplier
Fly through 10 zones
Fly through 15 zones
Visit every zone
Unlock Cardy the charismatic cardinal
Unlock Elly the energetic eagle
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