Here is the full list of all 40 ONE PIECE: PIRATE WARRIORS 4 trophies - there are 23 bronze, 13 silver, 3 gold and 1 platinum.
You won a battle with a Power type character for the first time
Cleared Dramatic Log “Introduction”
You used a special skill at least 10 times in one battle
You defeated your first enemy while in Form Change.
You stayed airborne for at least 10 seconds
You defeated 1000 or more enemies in a single battle
You defeated your first enemy using Full-Force Burst
You used a special skill for the first time
All trophies acquired
Cleared Dramatic Log “Alabasta Arc”
Cleared Dramatic Log “Enies Lobby Arc”
Cleared Dramatic Log “Summit War Arc”
Cleared Dramatic Log “Entry to the New World Arc”
Cleared Dramatic Log “Whole Cake Island Arc”
Cleared Dramatic Log “Land of Wano Arc (game original)”
Cleared at least 1 “East Blue” battle from the Treasure Log
Promoted to Treasure Log “Grand Line”
Cleared the Deciding Battle Episode from the Treasure Log “New World”
Achieved Battle Grade S in any episode
Unlocked at least 25% of the Gallery
Unlocked at least 75% of the Gallery
Collected 100 million or more berries in total
Collected 50 types of coin or more
Collected 10 or more playable characters
Collected 30 or more playable characters
One character's Crew Level has MAXED out
20 or more characters’ Crew Levels have MAXED out
Acquired 1 or more skills
Acquired 20 or more skills
One of your skill levels has MAXED out
One character's Action Growth Level has MAXED out
One character's special moves have all MAXED out
Acquired all the islands from "The Beginning Map"
You won a battle with a Speed type character for the first time
You won a battle with a Technique type character for the first time
You won a battle with a Sky type character for the first time
You used Power Dash 1000 times or more in total
Toppled 10,000 enemies during a Full-Force Burst
Toppled a total of 100,000 foes
Total Stage Objects Destroyed has exceeded 1000