Here is the full list of all 13 Star Wars: Jedi Starfighter trophies - there are 9 bronze, 3 silver and 1 gold.
Complete every mission on the Hard difficulty.
Complete every mission on the Medium difficulty.
Complete every regular and bonus objective for every mission.
Complete a mission without taking any damage.
Unlock all two-player Bonus Missions.
Complete every hidden objective.
Complete a mission using cooperative play.
Unlock every ship.
Unlock all one-player Bonus Missions.
Complete every mission on the Easy difficulty.
Complete all Act II missions on any difficulty.
Complete all Act I missions on any difficulty.
Complete all training missions.