Here is the full list of all 32 Dynasty Warriors: Strikeforce trophies - there are 12 bronze, 15 silver, 4 gold and 1 platinum.
Gained all Trophies.
Collected all Treasures.
Collected all Officer Cards.
Used all Card Tactics.
Collected all Weapons.
Collected all Chi Skills.
Collected all Orbs.
Completed all Quests.
Completed Shu's Story.
Upgraded all City Facilities to maximum.
Completed Wei's Story.
Collected all Legends.
Completed Chapter 6 in any Story.
Reached Level 50.
Completed Wu's Story.
Completed Chapter 4 in any Story.
Issued first command to Allied Officer.
Completed Chapter 3 in any Story.
Powered up first weapon.
Traded Officer with another player for the first time.
Used first Card Tactic.
Completed Chapter 2 in any Story.
Completed Chapter 1 in any Story.
Acquired first Chi Skill.
Made first Orb.
Made first weapon.
Defeated first Weaponry.
Completed first Quest.
Completed first online Quest.
Defeated first Officer.
Defeated first rank and file soldier.
Connected to Online City for the first time.