Here is the full list of all 20 War Theatre trophies - there are 7 bronze, 3 silver, 9 gold and 1 platinum.
Obtain all trophies.
Destroy three units in one turn.
Destroy four units in one turn.
Destroy five units in one turn.
Complete the Rat Mother story.
Complete the Sister Robyn story.
Complete the General Mort story.
Complete the WarHawk story.
Complete the Riven the Mad story.
Complete the Morena of Uld story.
Complete the AA-Team story.
Defeat the AI in a Skirmish game.
Complete one quest.
Complete five quests.
Complete ten quests.
Purchase one perk.
Purchase five perks.
Purchase ten perks.
Obtain 10000 gold from career quest rewards.
Obtain 25000 gold from career quest rewards.