There are 12 World Bosses to defeat in total, each of them spawning on a different month (so one boss per month). Each boss will spawn on the Wednesday of the first week of their attributed month (exception being the Black Dragon which spawns at the end of December), giving players a full week to farm the boss.

Bosses will have spawn locations distributed over either 1 or 2 outdoor adventure playfields (players in-game call these "instances"). Bosses have an estimated respawn time of 15 to 30 minutes and, once defeated in one instance, they will spawn in the next one.
These instances will have different names such as: Thor, Nu, Balder or Gamma.
Knowing beginner players and returning players may have trouble figuring out how to switch instances, here's how it works:
Once you know in which instance the boss will be in
1) Go to the respawn point closest to where the boss will be.
2) Click the orange arrow on the top right of your screen, located to the left of the mini-map.

3) Press "Select Instance" and then choose an instance.


The NPC who gives the Twelve Portents quest , The Astromancer, is located at (848,480) in Old Tarantia. You can also receive the quest by simply fighting one of the 12 bosses.

Upon completing the quest, you go back to the Astromancer and you get to pick 1 out of 4 Legendary cloaks, each with different stats (more on that later).

“Black wings shall mark the passing year,
with blood and shadows on the stone....”
— The Astromancer
Month: December

• Tarantia Noble District (880,730) - in front of Conan's Castle
  
• Tarantia Common District (480,940) - on the top of the cliff

“The Winter King spreads cold and fear,
among his snowy mountain home.”
— The Astromancer
Month: January

• Atzel's Approach (530,590) - near Black Dragon Magnus;
  
• Atzel's Approach (800,460) - on top of the ladder above the Halls of Eternal Frost;
  
• Conall's Valley (820,1040) - on the yeti plateau above the Mountain Groves resurrection point;
  
• Conall's Valley (1430,770) - in the Ymirish camp near Commander Magni.

“And in the narrow streets and ways,
death stalks with claws of ebony...”
— The Astromancer
Month: February

• Northern Grasslands, near the bridge towards Kara Korum in the north;
  
• Northern Grasslands (720, 1220) - just north of the Hole rez pad;
  
• Northern Grasslands, near the Red Cliff Inn on the eastern side of the playfield;
  
• Chosain Province, near the water just outside Gun Hai (the Scholars’ city in the northwest of the playfield);
  
• Chosain Province, near the water northeast of the Scholars’ tower on the northern side of the playfield.

“While Oldblood seeks and finds and slays,
amongst a southern, sand dune sea.”
— The Astromancer
Month: March

• Dragon's Spine (900, 650) - in the center of the map, in front of Otherworldly Junction and Palace of Cetriss

“And where the rivers meet and flow,
The Thrice Drowned wake to seek revenge...”
— The Astromancer
Month: April

• Thunder River (1310, 1650) - south of the graveyard, north of the Palisades rez pad
  
• Thunder River (1000, 570) - in the Wilds (green circle on the map, in the south of the playfield)
  
• Thunder River (500, 1300) - on one of the islands in the west of the playfield, a bit east of the outlaw camp

“And the Wyrm that is your oldest foe,
returns to battle once again.”
— The Astromancer
Month: May

• Eiglophian Mountains (640, 1160) - in front of Yakhmar's Cave
  
• Eiglophian Mountains (310, 1200) - in front of the entrance to The Vile Nativity
  
• Ymir's Pass (1190, 730) - in front of the Amphitheatre of Karutonia
  
• Ymir's Pass (960, 1300) - near the Temple of Ymir

“Then Nergal’s spawn reviled and lost,
comes to haunt the southern shore...”
— The Astromancer
Month: June

• Coast of Ardashir (775, 840) - island in the north
  
• Coast of Ardashir (660, 450) - near the logging camp

“While the offspring of Leviathus,
defiles the land and sky once more.”
— The Astromancer
Month: July

• Khopshef Province (490, 230) - crossroads
  
• Khopshef Province (290,380) - ruins
  
• Khopshef Province (780,240) - Black Castle
  
• Khopshef Province (790,550) - Caravanserai
  
• Dragon's Spine (560,970) - oasis

“And men who read what Skelos wrote,
will know what peril stalks the Isle...”
— The Astromancer
Month: August

• White Sands (690,590) - in front of the Ancient Temple

“And where the dead men rot and bloat,
The Lurker rises, most reviled.”
— The Astromancer
Month: September

• Field of the Dead (560,1260) - at the entrance of House of Crom
  
• Eiglophian Mountains (190,1280) - at the entrance of The Vile Nativity

“Seekers search the untamed wild,
to find the Queen of empires past...”
— The Astromancer
Month: October

• Wild Lands of Zelata (250,540) - south of Tesso

“And searching where the ring is strongest,
face the Lord of fire at last.”
— The Astromancer
Month: November

• Kheshatta (1125,865) - East Ruins
  
• Kheshatta (1130,435) - Caravan Raiders Camp
  
• Kheshatta (700,180) - Ghanatan Camps (oasis)
  
• Kheshatta (260,640) - Black Ring Explorers (bats)

As stated before, upon completing The Twelve Portents quest, you earn yourself a legendary cloak. You'll be offered four different cloaks so choose the one that has the better stats for your class.
Which four cloaks you get to choose from depends on your character's archetype (Rogues, Soldiers, Priests or Mages).

Here are all the cloaks offered to each archetype:
(You'll notice that some archetypes are offered the same cloaks)

Rogues:

Soldiers:



Priests:

Mages:

These relics drop from the Portents, you get 1 per boss (meaning only 1 per month). They can be traded for items with the Keeper of Portent Relics in Old Tarantia, (847, 487) located down the stairs below The Astromancer.

Once you've accumulated enough relics, you can purchase: Companions and Mini-Pet versions of the Portents or a Slayer's Cache of the Portents, which mainly drops Tier 3 tokens (Simple Relic III), but can also drop interesting loot like epic rings, talismans, necklaces and any of the Mini-Pet/Companion bosses.

Every time you participate in defeating a world boss, you'll always receive a chest which will give you a reward. There are two types of chests you can earn:

The Slayer's Cache, an epic chest with a small chance to drop.

This chest tends to drop Tier 3 tokens like the Simple Relics III and the Rare Relic.
You can also get a mini-pet/companion version of the boss or an epic item (necklace, ring, etc).

Or the Hunter's Trove, a rare chest which is guaranteed to drop unless you receive an epic chest.

The Hunter's Trove offers a much wider set of possible rewards like social armor sets, Tier 1 or Tier 2 raid gear and weapons, AA Mastery XP, Khitai tokens, common or rare pets.
If you're unlucky you get potions or elixirs that have funny effects on your character.
Note that certain social armor sets are regional and only drop if the world boss is in a specific region (Cimmeria, Aquilonia, Stygia, Khitai, Barachan Isles).
Here's some of the social armor sets:
Barachan Corsair

Harlot

Slayer

Titan Killer

Black Leather

Fallen Leviathan

Hero Ascendant

Shattered Colossus

Heaven’s Lake

Sanctum of Atlantis

Hyperborean Shaman

Khemi Guard