Here is the full list of all 16 Under Siege trophies - there are 3 bronze, 2 silver, 10 gold and 1 platinum.
Gain all trophies
Win 5 ranked matches in a row
Win a ranked match in less than 5 minutes
Win an online match with a friend
Create a map
Complete the game in the Hard difficulty setting
Complete Chapter 5
Complete Chapter 4
Complete Chapter 3
Complete Chapter 2
Heal a total of 20000 hit points
Accumulate 5000 gold
Kill 1000 enemies
Complete a chapter without losing a single unit
Complete Chapter 1
Complete the tutorial