Tails Spin - Lestallum
First Available: Chapter 3
Other Requirements: Complete Ace of Carapace
Rewards: 2,000 EXP
In order to accept this quest from the Arms Vendor in Lestallum you'll need to first complete the story quest, "A Stroll for Two" in the city. Once you've completed this quest, all of the available side quests in Lestallum become available. Note: If you're having trouble accepting the quest from this NPC, you actually have to interact with the counter in front of him and not the NPC itself to accept/turn in these quests.
For this quest you'll need to travel to the location marked on your map and defeat the Spiracorn enemies here. They're right along the beach and mixed in with some crab enemies, it shouldn't be too difficult of a fight for you. Defeat them and then return to the NPC in Lestallum to turn in the quest.
Completion of the Tails Spin quest will open up the final quest from this NPC which is Sting Your Praises.