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