Here is the full list of all 27 Stardust Vanguards trophies - there are 12 bronze, 7 silver, 7 gold and 1 platinum.
Unlock all other Trophies
Lose an entire war to the Pirates.
Assassinate a VIP unit.
Complete all 30 survival waves in endurance mode.
Get a tri-kill.
Unlock all arenas, stadiums, and game modes.
Complete all 9 survival waves on hard difficulty.
Complete all 9 survival waves on medium difficulty.
Complete all 9 survival waves on easy difficulty.
Get a "Pyrrhic Victory" post-battle status (win with the most troop losses).
Complete a round in "Stadium Epsilon"
Play a match of Space Ball
Get a "Most Boring" post-battle status (have no other statuses).
Complete a round in the "Colony Attack" arena.
Play a custom battle with insane amounts of reinforcements
Win a single battle as the yellow team.
Play a custom battle with infinite ammo.
Complete a round in the "Grid" arena.
Win a single battle as the blue team.
Call a 100 RP squadron into battle
Win a single battle as the red team.
Deflect a bullet into another Player.
Get a "Sacrifice" post-battle status (your team won while you were eliminated).
Get an "Honorable" post-battle status (never fire bullets).
Complete a round of deathmatch
Win a round while also being a bounty target.
Win a single battle as the green team.