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Vendor: Guillermel, Caravan
Quest Name: "Nomadic Needs"
Quest will pop up pretty quickly after you defeat the first Ghulture boss.
Badge Needed: Treasure Hunter Badge
Badge Requirement: Sell 100 Antiquities aka Shinies to Guillermel
You can farm for shinies all over Mirage. It is usually found on the ground like stone blocks, parchment, etc. It is pretty easy to find. It's a bright light twinkling at you. It's very hard to miss.
Gold Price: 100k Gold

Vendor: Robin, Aggrobah
Quest Name: "The Warriors"
The quest will pop up after you finish Aggrobah. The last quest will be Truce Talks.
Badge Needed: Aggrobah Sheriff Badge
Badge Requirement: Defeat 100 Rival Gang Members (Thuggie Goons)
Gold Price: 100k Gold

Vendor: Captain Kettay
Quest Name: "Tabbi Loyalist"
I'm not sure when this quest pops up, but I saw it available when I was in Instaboa. However, it could have popped earlier. 
Badges Needed: Tabbi General Badge & Wurmslayer Badge
Badge Requirement: Defeat 100 House Purrzian Assailants & Defeat 100 Sand Wurmling
Gold Price: 100k Gold

Vendor: Destro-uctor, Istanboa (He will show up when you finish the last quest in Istanboa, "The Aridian Chronoshard")
Quest Name: "Serpentine Revolution"
This quest will be available right away once you unlock him after the last quest in Istanboa.
Badges Needed: Serpentine Avenger Badge & Dunes Veteran Badge
Badge Requirement: Defeat 100 Calixco Guards & Defeat 100 Sand Djinns
Gold Price: 100k Gold

Vendor: Advisor Francy Fries, Rubal Wastes (She will show up when you finish the quest in Rubal Wastes, "The Baron's Last Stand")
Quest Name: "Calixco Rising"
This quest will be available right away once you unlock him after the last quest in Istanboa.
Badges Needed: Unconstrictable Badge & Vipers' Bane Badge
Badge Requirement: Defeat 100 Boas & Defeat 100 Vipers
Gold Price: 100k Gold

Vendor: Prefect Josapat, Yakhal Mountains (He will show up when you finish the quest in Yakhal Mountains, "Breaking The Hardline")
Quest Name: "Sayameez Security"
This quest will be available right away once you unlock him.
Badges Needed: Sandwitches' Scourge Badge & Rebellion Crusher Badge
Badge Requirement: Defeat 100 Sandwitches & Defeat 100 Bumbai Rebel Soldiers
Gold Price: 100k Gold