There are 20 Trophies that can be earned in this title.

Bronze

RickRolled
Destroy the enemy castle with a boulder.

Cooking by the Book
Complete the Viking campaign.

V for Veggies
Complete the Aztec campaign.

I'm not kung, Fool!
Complete the Chinese campaign.

Uncontrolled Demolition
Destroy a tower under construction with Rage.

Bull in a China shop
Cast a boulder that does not damage a single unit.

Son of Norris
Kill 36 units with a single unit.

Techno Viking Dances Away
Reach the maximum distance in a Berserker Run game.

At First I Was Afraid
Survive over 30 minutes in a Survival game.

King of the Stone Age
Kill all Vikings in a Boulder Mode game without killing any of your own.

Lacking Balls
Complete Aztec Campaign level 8 without using a Boulder.

Fourtification
Complete Viking Campaign level 7 with all Towers intact.

Pity the Fool!
Survive Viking Campaign level 10 without the help of Mr. Thor.

Where are the Kangaroos?
Complete Viking Campaign level 4 by destroying the enemy base.

Fort Knox'd
Prevent the Giant in Aztec Campaign level 2 from reaching the Goldmine.

Keep Your Lousy Army
Complete Aztec Campaign level 10 without taking control of the Viking army.

Planet of the Ninja Apes
Complete Chinese Campaign level 4 without a single Ninja death.

Blotting out the sun
Complete Chinese Campaign level 7 wth 17 or more Rocketeers alive.

Lost Vikings
Complete Chinese Campaign level 8 without killing a single Berserker.

Silver

Social Viking
Play 10 matches online.

http://www.ps3trophies.org/game/swords-and-soldiers/trophies/