Here is the full list of all 46 Fortnite trophies - there are 32 bronze, 10 silver, 3 gold and 1 platinum.
Complete "All Together Now" (Daily Quest)
Destroy 100 Garden Gnomes in successful missions
Loot 300 Treasure Chests in successful missions
Complete "Canny Valley Storm Shield Defense 1"
Complete all the Main Quests in Plankerton
Complete "Plankerton Storm Shield Defense 6"
Complete "Toxic Treasures - Stage 10"
Complete "I'm Probably Dead"
Complete "Defender Training - Stage 2"
Complete "Epic Troll Stash"
Complete "The Battle of Plank Harbor"
Complete "Shelter Skelter"
Complete "Rifty Business"
Complete "Six Minutes"
Complete "Ray.README"
Complete "Survivor Training - Stage 2"
Complete "Two Swirls"
Complete "Weapon/Trap Evolution"
Complete "Hero Training - Stage 2"
Complete "Plankerton Storm Shield Defense 1"
Complete all the Main Quests in Stonewood
Complete "Homebase Storm Shield Defense 6"
Complete "Rescue the Survivors"
Unlock and Slot your first Storm Shield Defender
Unlock and Slot your first Mission Defender
Complete "Retrieve the Data"
Complete "Ride the Lightning"
Complete "Before and After Science"
Unlock access to the Outlander Hero
Unlock access to the Ninja Hero
Complete "Homebase Storm Shield Defense 1"
Unlock access to the Constructor Hero
Complete your first mission
Protect the survivors
Craft your first weapon
Earn all other Fortnite trophies to collect this trophy
Complete "Quad Squad"
Complete "Canny Valley Storm Shield Defense 6"
Complete all the Main Quests in Canny Valley
Complete "Twine Peaks Storm Shield Defense 1"
Complete "Twine Peaks Storm Shield Defense 6"
Build 500,000 Structures in successful missions
Save 10,000 Survivors in successful missions
Fully explore 1,500 zones in successful missions
Kill 20,000 Mist Monsters in successful missions
Complete 1,000 Play With Others missions