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.
Master one level.
Collect every coin in a level (excluding bonus area coins)
Complete Boot Camp.
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 all levels.
Complete the RageQuit Rex mode.