Main Walkthrough 

Location: Nanohana
Participants: Luffy, Usopp, Zoro
Reward: Luffy, Zoro, and Usopp's Bond Art, Shock Element Jewelry

Likely to be the second Memory Link you encounter in One Piece Odyssey, An Evil Deed is unlocked once you've completed the events of Alabasta. Make your return trip to Waford, then proceed through the story until it kicks you back into Alabasta. The Frayed Memory will appear on the map in Nanohana, at the top of a jump point near the connecting gate between the north and south ends of the town. It's right across from a small fountain.

(Given the appearance of a specific NPC in this quest, it's possible that you also need to complete the Side Story The Truth About Eye-lashes before this Frayed Memory will appear. Honestly not sure.)

Part I

Hop to the ground. You'll see a Strange Merchant near the fountain with the telltale ring floating over his head. His name's Otogin, and he'll cheerfully give the group a weird mushroom, asking that Zoro eat it. Not at all suspicious. Zoro, gullible to the end, will scarf it down... and collapse, because of course.

Usopp will recall Chopper mentioning a moss in Alabasta that can cure poisoning. Luffy will charge off, leaving Usopp to care for Zoro. Head to the Western Lagoon, out of Nanohana's southwestern gate, and Luffy will run into Eye-lashes, the camel with the excellent eyelashes. He'll guide Luffy to the moss.

Return to Usopp and Zoro in the center of Nanohana. You'll find Usopp being menaced by three weapon-wielding men who clearly have it out for Zoro. Luffy and Usopp will need to fight off the three Thieves. Luffy can beat down Thief A and B, while Usopp is better suited to Thief C. Once the Thieves are gone the Frayed Memory will resolve itself, but... you won't be done just yet.

Part 2

When you pop out of the Hysteria and regain control of the party you'll see a blue-tinged man sitting nearby. He'll point you towards an alleyway. Head north through Nanohana to the Spice Bean, down the western road, and then south down the length, shady alleyway on the west side of town. The Frayed Memory is at the far south end of the alley.

The team will pop out and find Otogin speaking to the shady fellows you beat up earlier. You'll need to beat the three Thieves up again, and with Zoro in the party this fight is even easier than the last one. After the fight Otogin will explain his situation, and will beg the Straw Hats to help him deal with his unscrupulous brother.

Head back to the gate where the first Memory Link began. Another band of Thieves is waiting, larger than the first, and they'll attack. Fighting this group shouldn't be much more difficult than fighting the first. A third group will show up once you win the second battle, headed by Otogin's brother, and they, too, will attack. Your team will learn the Bond Art Gum-Gum Dragon Fire Pistol Twister Star, and using it will wipe out most of the competition. You shouldn't have any trouble defeating Anikin and the remaining goons once the move goes off.

Defeating Anikin and his lot will end the Memory Link in your favor, and the two brothers will reconcile. D'aw.