There are 29 Trophies that can be earned in this title.

Bronze

For God and King
Win first battle as English

For the Fleur de Lis
Win first battle as French

The First Step
Recruit first troop

Tactician
Complete a flanking maneuver

All Around the World
Get a unit into each corner of the screen

Silver

Power in Numbers
Recruit max number of units

Best 2 of 3
Win a Short Tug of War

Best 5 of 7
Win a Long Tug of War

Conquer the Playground
Win a Sandbo Match

Serf
Kill 500 troops

Knight
Kill 1000 troops

Vassal
Kill 2000 troops

Mounted Unit to Level 10
Get a mounted unit to level 10

Knights to Level 10
Get a knight unit to level 10

Infantry to Level 10
Get a infantry unit to level 10

Archers to Level 10
Get a ranged unit to level 10

10 Heads are Better than One
Recruit 10 units

Master Strategist
Win a level with all unit types

Let the Battle Begin
Complete the Tutorial

Invincible
Win a battle without losing a unit

Gold

Glory to the English
Win the English campaign

Defender of the Crown
Win the French campaign

Prince
Kill 5000 troops

King
Kill 10000 troops

Platinum

Medieval Master
You have successully unlocked all of the trophies.

4 Secret

http://www.ps3trophies.org/game/history-great-battles-medieval/trophies/