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