Legendary loot in Borderlands 3 is difficult to find. Bosses can only be farmed after you defeat them in the main story or on a side quest. After that, you are free to fight them as much as you want.
Note: If you don't get the loot you want after defeating a boss, you can always return to Sanctuary or restart the game.
Legendary items are rare and have a low percentage rate of dropping, so be prepared to fight a boss and not get the loot you want.
Legendary Boss Loot in Borderlands 3
Mouthpiece (Chapter 3: Cult Following) - Mind Killer (Shotgun)
Gigamind (Chapter 3: Hostile Takeover) - Smart-Gun XXL (SMG)
Katagawa Ball (Chapter 8: Space Laser-Tag) - Tsunami (SMG)
The Rampager (Chapter 10: Beneath the Meridian) - Stuffed Quadomizer (Rocket Launcher)
The Rampager (Chapter 10: Beneath the Meridian) - Lead Sprinkler (Assault Rifle)
GeniVIV (Chapter 14: The Family Jewel) - Messy Breakup (Shield)
Aurelia Hammerlock (Chapter 16: Cold as the Grave) - Frozen Heart (Shield)
Troy Calypso (Chapter 19: The Great Vault) - Occultist (Pistol)
Tyreen the Destroyer (Chapter 23: Divine Retribution) - King's Call (Pistol), Queen's Call (Pistol)
Killavolt (Kill Killavolt - Side Mission) - Shocking 9-Volt (SMG)
Unique Legendary Loot Drops
Unique enemies can be played against at any point in the game as long as you have access to their areas.
Lavender Crowley (The Droughts, Pandora) - Bankrolled Predatory Lending (SMG)
Skrakk (Ascension Bluff, Pandora) - SkekSil (Pistol)
Chupacabratch (Athenas) - ChupaChupa's Organ (Grenade Mods)
One Punch Psycho (Lectra City, Promethea) - One Pump Chump (Shotgun)
Jabbermogwai (Voracious Canopy, Eden-6) - Hellfire (SMG)