Here is the full list of all 16 JumpJet Rex trophies - there are 11 bronze and 5 silver.
Defeat the third boss.
Defeat the second boss.
Defeat the first boss.
Complete Boot Camp.
Collect every coin in a level (excluding bonus area coins)
Defeat the fourth boss.
Complete adventure mode on easy.
Complete adventure mode on normal.
Live to Fly another day.
Pay the ultimate price.
Collect every coin in every level (excluding bonus area coins)
Complete the SpeedRun mode and post a time to the leaderboard.
Collect all the hidden items.
Master one level.
Master all levels.
Complete the RageQuit Rex mode.