Here is the full list of all 13 Trans-Galactic Tournament trophies - there are 9 bronze, 3 silver and 1 gold.
Reach Level 30
Earn 500 KO blows
Reach Level 20
Win 25 games
Earn your first weapon
Socket your first Badge
Win an Annihilation game while dying a maximum of 2 times
Reach Level 10
Defeat all members of an opposing team at least twice in any game mode
Win a Conquest game without giving your opponent more than 50 points
Socket your first Workout
Win your first game
Win a Plunderball game where the opposing team wins no points