Here is the full list of all 13 Castle Invasion: Throne Out trophies - there are 9 bronze, 3 silver and 1 gold.
Complete Level 1
Defeat the King's Dragon
Defeat the King's Troll
Defeat the Evil Archer
Defeat the King's Commander
Defeat the King!
Fully Upgrade the Bow
Fully Upgrade the Spear
Fully Upgrade the Crossbow
Unlock all Upgrades!
Collect 50 Stars
Collect 100 Stars
Collect 150 Stars