In Fortnite, like most games these days, you will earn a number of Achievements simply by doing specific things within the game. For each Achievement you accomplish, you will earn a given number towards your GamerScore. In total, there are 45 different Achievements for players to obtain. Below is a list of all the achievements found in Fortnite, along with the method of which to unlock them.
Achievements & Methods
Gunsmith (10G): Craft your first Weapon.
Take Out Those Husks (10G): Protect the survivors.
Some Sort of Rocket (10G): Complete your first Mission.
Shelter From the Storm (10G): Complete "Homebase Storm Shield Defense 1".
Constructor Leadership (10G): Unlock access to the Constructor Hero.
Before and After Science (10G): Complete "Before and After Science".
Ride the Lightning (10G): Complete "Ride the Lightning".
Hired Gun (10G): Unlock and slot your first Storm Shield Defender.
Man on a Mission (10G): Unlock and Slot your first Mission Defender.
Retrieve the Data (20G): Complete "Retrieve the Data".
Rescue the Survivors (20G): Complete "Rescue the Survivors".
Can You Feel that Shield Power? (20G): Complete "Homebase Storm Shield Defense 6".
Launch the Rocket (20G): Complete all the Main Quests in Stonewood.
Epic Troll Stash (20G): Complete "Epic Troll Stash".
Walk the Plank! (20G): Complete "Plankerton Storm Shield Defense 1".
Two Swirls (10G): Complete "Two Swirls".
Ray.README (10G): Complete "Ray.README".
Wow, I'm Inside! (20G): Complete "Six Minutes".
Gotta Get Rifty (20G): Complete "Rifty Business".
Shelter Skelter (20G): Complete "Shelter Skelter".
Liberation! (20G): Complete "The Battle of Plank Harbor".
Crank Up the Gain (20G): Complete "Plankerton Storm Shield Defense 6".
Many Planks (30G): Complete all the Main Quests in Plankerton.
Future Days (30G): Complete "Canny Valley Storm Shield Defense 1".
Quad Squad (20G): Complete "Quad Squad".
Amped for Expansion (30G): Complete "Canny Valley Storm Shield Defense 6".
Uncanny! (40G): Complete all the Main Quests in Canny Valley.
Into the Night (40G): Complete "Twine Peaks Storm Shield Defense 1".
All Tied Up (50G): Complete "Twine Peaks Storm Shield Defense 6".
Become a Superhero (20G): Complete "Hero Training - Stage 2".
All Together Now (20G): Complete "All Together Now" Daily Quest.
Survivor Specialist (20G): Complete "Survivor Training - Stage 2".
Proven Defender (20G): Complete "Defender Training - Stage 2".
Outlandish! (20G): Unlock access to the Outlander Hero.
Dragon Slash! (10G): Unlock access to the Ninja Hero.
Darwin Rewards (20G): Complete "Weapon/Trap Evolution".
Evil Things with Crazy Teeth (30G): Complete "Toxic Treasures - Stage 10".
Talented Builder (40G): Build 500,000 Structures in successful Missions.
Go Gnome! (30G): Destroy 100 Garden Gnomes in successful Missions.
Guardian Angel (50G): Save 10,000 survivors in successful Missions.
Loot Legend (30G): Loot 300 Treasure Chests in successful Missions.
World Explorer (40G): Fully explore 1500 zones in successful Missions.
Unspeakable Horrors (40G): Kill 20,000 Mist Monsters in successful Missions.
Plays Well with Others (50G): Complete 1000 Play With Others Missions.
… Oops. (20G): Complete "I'm Probably Dead".
Hero of the Storm: Unlock all other Trophies.