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
Complete a chapter without losing a single unit
Complete the game in the Hard difficulty setting
Complete Chapter 5
Accumulate 5000 gold
Win an online match with a friend
Complete Chapter 4
Complete Chapter 3
Kill 1000 enemies
Complete Chapter 2
Heal a total of 20000 hit points
Create a map
Complete Chapter 1
Complete the tutorial
Win 5 ranked matches in a row
Win a ranked match in less than 5 minutes