Here is the full list of all 12 Lost Wing trophies - there are 11 gold and 1 platinum.
Get all the trophies
Completed the Tutorial
Unlock a new color for your ship
Destroy 5 obstacles with a bomb
Fight a boss
Fire 1000 bullets
Destroy 100 obstacles
Arrive to a checkpoint untoched
Score at least 100K points in any level
Crash your ship
Play upside down
Lose a wing