Location: Dressrosa City Area
Participants: Nami, Franky, Brook
Reward: Nami, Franky, and Brook's Bond Art, Death's Edge Power Jewelry
In order to unlock this Memory Link you must first complete the main story events surrounding Dressrosa, up to and including the defeat of Doflamingo. When you return to Dressrosa in Chapter 9 a bunch of side content - including this Memory Link - will be unlocked. You can find the Frayed Memory inside the single, broken home on the north side of Square, At Fountain. There's a Yoisa Sign that will put you right beside the house.
Part 1
This time around it will be Nami, Franky, and Brook exploring Hysteria. They'll discover the bearer of the ring quickly, this time, but it's... a violin? The team decides that they need to reunite the instrument with its owner. Better start talking to people.
There are a number of folks in the vicinity to talk to, but only two of them offer hints: A merchant to the north and a woman on the hunk of raised road beside the fountain. Speak to both of them to learn a bit, but... nothing useful. Brook decides to try a different tactic and play the instrument. Walk to the chasm to the east of the Bored Merchant and he'll give it a try. The sound attracts a bunch of people...
... including two Sailors. Beat them up with Nami and Franky. More will show up, including a Navy Officer, though Nami and Franky should have more than enough firepower to take them out. Brook will discover the owner of the violin... or their daughter, Roche, anyway... and this section of the Memory Link will end on a sad note.
Part 2
The second Frayed Memory is located in "Old" Royal Plateau Area, in the northwest of Dressrosa. You can get there quickly by jumping to the Coliseum Path Yoisa Sign, then walking north down Blacksmith Road. The Frayed Memory is in front of a pink house on your right as you walk east.
Trek back to the chasm where Brook played last time, at the south end of Coliseum Path. The Straw Hats will run into a marine barricade, and you'll need to fight a guy named Rear Admiral Bufflo and his goons. Your team has plenty of AOE attacks to make this an easy fight, and Nami can go the extra mile with Happiness Punch to Charm her attackers.
Go all the way back to the chasm near Square, At Fountain to find Roche playing the violin. She'll be accosted by two marines (to be fair, one of them is pretty nice), who will then attack the team. You'll learn Soul Franky Swing Arm Boxing, which you can use to very quickly wipe out the marines. The trip to Hysteria will end shortly thereafter, and you'll earn your reward.