[-] Find the book thief
Fast-Travel to Akane Beach and head to the marked location. The area where you have to go has an obstacle that requires 10,000 damage to clear. Make sure you have your Fairy Gauge full so you can trigger a Magic Chain and deal Over Damage. It will also help saving before attempting to clear this obstacle, just to be safe. In case your Fairy Gauge is not full, consider fighting enemies AWAY from the obstacle to fill it up. Once the obstacle has been cleared, head to the marked location to find the thieves and defeat them in battle.
[-] Gather all of the book’s pages
After the battle, the pages of the book will be scattered in the immediate area. Their locations will be marked on the map as well so go ahead and collect all the pages. Finally, report back to the inn to complete the quest.
[-] Gather information in town
[-] Expose the smuggling ring
Leave the inn and talk to the marked NPCs in town to get some intel. Next, travel to the Capital Highway and head to the marked location to find the smugglers. Defeat them in battle then report back to the inn to complete the quest.
[-] Recover the precious metals
Gajeel and Lucy will be required characters for this request but you can still add two more party members if you want. Since you just got Gajeel, this will be a perfect time to test his abilities. Make sure your team’s Lacrima is properly set up then head out to the Capital Highway.
Once there, pick up the metals from the marked gathering points and defeat the marked enemies as well until you collect all the metals. Report back to the inn to complete the quest.
[-] Pick up the trash on the ground.
Leave the inn and pick up the trash from the gathering points that will appear in order. After picking up the third trash, you’ll encounter bandits and this will trigger a battle. Wipe them out easily and the objective will update.
[-] Fight off the thieves.
Find the bandits as marked on the map and hit them with your sword to engage them in battle. Continue wiping off the bandits as they appear on the map. After defeating all of them, report back to the inn to complete the quest.
[-] Take down the Mimic.
Head to the Capital Highway and continue to the marked location. After the short cutscene, attack the man with the marker to trigger a battle against the mimic. This enemy is weak against Light so have Lucy use Summon Leo to greatly damage this enemy. After getting defeated, the mimic will flee to another location.
Go to the marker and talk to the boy on the right side to trigger another battle. Like before, have Leo wreck the mimic to force it to flee once again. Finally, head to the third location and talk to the man on the right side to trigger the last battle. Defeat the mimic then report back to the inn to complete the quest.
We have questions and answers related to this topic which may also help you: