Parts of this side quest can be completed as you progress through the game, but it cannot be fully completed until after you have reached the Balfonheim Port.
This side quest is also known as the Nabreus Medallions side quest and it allows you to obtain the optional Esper named Chaos once you reach the end.
The quest involves locating three Medallions and using them to access three locked rooms in the Necrohol of Nabudis.
In order to begin the quest, you will need to complete a few Hunts, including:
After you defeat the Wraith during Hunt 04, you will gain access to one of the houses in Lowtown. There is a 
Dusty Letter sitting on the desk that you need to pick up.
This letter details the order that you need to operate the Sluice Gates in once you reach the Garamsythe Waterway – but this guide has all of the details so you will not need to refer to the letter. You will, however, still need it to complete the side quest.
Defeating White Mousse will result in you obtaining the Broken Key at the end of the battle. The petitioner, Sorbet, will take the broken key and give you the Sluice Gate Key allowing you to operate the Sluice Gates.
Finally, defeating Orthros will result in you obtaining a Blackened Fragment at the end of the battle. You now need to obtain the other two Fragments in order to obtain the first Medallion; specifically, the Dull Fragment and the Grimy Fragment.
Travel down to the Garamsythe Water from the North Sprawl of Lowtown. Head down to the Garamsythe Water and into the Central Waterway Control area.
Make sure that all the switches are turned off before you start by making sure that none of the lights are on. From there, activate the following switches:
Once all five switches have been flipped, in the order listed above, you will hear a faint noise of something dropping on the ground. Search the area to the south (across the water) for a shiny object which is the Dull Fragment.
The last fragment involves some interaction with creatures known as the Nu Mou. For starters, you must speak to a Nu Mou named Roh’kenmou who can be found up in the Nabreus Deadlands.
Travel to the area in the south with the Save Crystal called the Muted Scarp (use the map below for reference). Talk to him and select all of the possible choices. After speaking to him here, he will now appear at Old Dalan’s place in Lowtown.
Travel to Rabanastre, into Lowtown and head to Old Dalan’s house. Speak to Roh’kenmou again and he will tell you about a “most important object” that he needs help finding, a Medallion.
While you are at Old Dalan’s, you can hand over both of the two Fragments to Roh’kenmou if you’d like as you will be handing all three over to him eventually.
Head back out into Lowtown. You will already be in the South Sprawl but travel east to one of the southeast corners and search for a child named Filo. Speak to Filo and then head back up to Rabanastre.
Search the Southern Plaza area for the “Curious Woman” and speak to her as well.
The next destination is the Muthru Bazaar. Speak to one of the Bangaa Merchants on the right side of the passageway and he will tell you about the necklace that the Curious Woman was talking about and that he sold it to an Imperial Soldier.
Travel to Yugri’s Magicks shop in the East End of Rabanastre and speak to the Sotted Imperial kneeling over in the corner. Ask him about the necklace and then tell him about the woman near the fountain.
Go back down to Lowtown and search for Kytes in the North Sprawl area just outside of Storehouse Five.
Finally, seek out Filo one more time and when she asks “did you need something, Vaan?” choose to respond with “I need to see this woman.” A short cutscene will take place in Yugri’s Magicks shop and you will receive the Grimy Fragment.
Return to Old Dalan’s and speak to Roh’kenmou again. Hand him all three Fragments and he will tell you that they make up the Medallion of Bravery. He then implores you to travel to Nabudis explaining that the Nu Mou may have found a new Medallion bearer (you).
The second Medallion is located in Old Archades. The first step in obtaining it involves speaking to Roh’kenmou in the Imperial City of Archades in Charlotte’s Magicks shop.
Again, Roh’kenmou will only appear if you have spoken to him already in the Nabreus Deadlands. Roh’kenmou will explain that he sold the Medallion to a person named Otto.
Travel out to Old Archades and search the northern area of the Alley of Muted Sighs. The “Proper Gent” that you may have spoken to previously is actually Otto. He explains that he is giving his fiancé a ring made out of Moonsilver and that he has taken a small piece of the Medallion.
He then hands over the rest to you. Return to Roh’kenmou in Charlotte’s Magicks and give him the Moonsilver Medallion.
The last Medallion can be obtained by returning to the Nabreus Deadlands to the Muted Scarp where you first met with Roh’kenmou. This time there will be a small gathering of Nu Mou creatures.
Speak to Ma’kleou again and they will tell you that they plan to give you the Three Medallions, however you must travel to the “Overlooking Eternity” area to retrieve the final Medallion. You may recall this area as the same place that you fought Roblon if you have completed Hunt 18: Adding Insult to Injury (Roblon – Rank VI).
To reach Overlooking Eternity, travel to the northwest corner of The Slumbermead and search for a hidden pathway that goes north and which does not appear on the mini-map. Follow the pathway through The Fog Mutters and on to Overlooking Eternity.
Even if you are familiar with this area and have been here before, be careful heading up the pathway as it is very easy to become overwhelmed by Dead Bones enemies no matter what level you are. They respawn very quickly.
Approach the pedestal at the top of Overlooking Eternity to initiate a short cutscene. You will receive the Medallion of Bravery, the Medallion of Love and the Lusterless Medallion once the cutscene has completed. These three medallions can be used to open doors in the Necrohol of Nabudis and eventually obtain an optional Esper named Chaos, Walker of the Wheel.
Check out the Necrohol of Nabudis side quest section for more information about the accessing the three bosses as well as a number of other side quests available in the zone:
This side quest is complete once you have obtained the three medallions from the pedestal atop the ridge at Overlooking Eternity.
