Here is the full list of all 30 Nobunaga's Ambition: Taishi trophies - there are 14 bronze, 10 silver, 5 gold and 1 platinum.
Clear 10 quests
All diplomacy commands have been used
Achieve a 100,000 gold income
Construct a new castle
The population of your clan reaches 1 million
Upgrade a castle to its maximum
Experience all disasters
Win a battle with an opponent who has more than double the soldiers
Win a historical battle
All agriculture commands have been used
Win a battle with none of your units retreating
Enact 30 policies
Use each of the various policies: agriculture, commerce, military, and rhetorical
All commerce commands have been used
Form an alliance
All records of "NOBUNAGA'S AMBITION: Taishi" are cleared
You receive a wife through a marriage alliance
Win a battle on sea or lake
Win a battle as part of a coalition
Obtain 5 grand trading zones simultaneously
Win 50 battles
Clear the scenario "Kawagoe Night Raid"
Clear the scenario "The Battle of Itsukushima"
Clear the scenario "The Battle of Kawanakajima"
Clear the scenario "Dawn of Revolution"
Clear the scenario "The Battle of Takagi River"
Clear the scenario "Like a Dream"
Use 20 types of plans in battles
Unlock all of the resolve traits for 5 Daimyo
Clear the game by destroying all clans