If you want to know how to get the medallions that allow you to fight Humbaba Mistant, Fury and Chaos, here's how. First, you need to complete the "Lost in the Pudding" (White Mousse), "Waterway Haunting" (Wraith) and "Crime and Punishment" (Orthros) hunts. When you complete the "Crime and Punishment" hunt, you will obtain the Blackened Fragment as a reward. Go into the house that the kid came out of after you completed the "Waterway Haunting" hunt and examine the desk to obtain the Dusty Letter. Read it and it will tell you a sequence. Go to the Garamsythe Waterway and do the following in this order (note that you also need the Sluice Gate Key, which is obtained by talking to Sorbet again after giving him the Broken Key you got from doing the "Lost in the Pudding" hunt): turn on No. 11, turn on No. 4, turn off No. 11, turn on No. 3 and finally turn off No. 4. If done correctly, you will hear a noise. Search for the sparkle on the ground and examine it to obtain the Dull Fragment. Now, head to the Nabreus Deadlands and talk to Ma'Kleou (if he's not there, it means you've already talked to him). Head to Old Dalan's house in Lowtown, Rabanastre and talk to Roh'Kenmou there. Then go to the south-east area of Lowtown and talk to Filo. Go next to the Southern Plaza of Rabanastre and talk to the Curious Woman looking at the fountain. Go to the Muthru Bazaar and ask all the merchants there about the necklace. Then go to the Magick Shop and talk to the Sotted Imperial sitting in the corner. Pick the first option twice. After that, head back and talk to Filo and choose "Let's go." to obtain the Grimy Fragment after some events. Talk to Roh'Kenmou again and he will leave. Next step is to head to Archades. Once there, go to the Magick Shop, where Roh'Kenmou will be. Talk to him, then head to the Alley of Muted Sighs area of Old Archades and talk to the Proper Gent sitting on the wall on the eastern side (his name is Otto). He will give you the Moonsilver Medallion. Head back to Roh'kenmou and give him the medallion. The last step in this quest is to head to the Nabreus Deadlands again. Go to The Slumbermead and look for a secret path heading northwest from the area. At the end of the path, talk to the Nu Mous and they will give you the Medallion of Bravery, the Medallion of Love and the Lusterless Medallion.
The Medallion of Bravery can be used in the Necrohol of Nabudis, in the area named Cloister of Distant Song. Use it to open the Door of Horrors and fight Humbaba Mistant. Use the Medallion of Love to open the Door of Loathing in the Hall of the Ivory Covenant area and fight Fury. After you defeat those two, the Lusterless Medallion will change into the Medallion of Might. Use that to open the Door of Despair in the Cloister of Distant Song area and fight Chaos.