Unlike Van, Interrupted, Ace of Carapace is the first quest you can trigger from the arms vendor in Lestallum.
The only requirements you need to meet for this mission is to finish Burden of Expectation story-quest, which will lead you to the main city in Duscae, and to finish A Stroll for Two.
Once you finish both quests, look for the arms vendor to start Ace of Carapace.
The vendor will inform Noctis that he needs the carapace of a Bulette, a beast you will have to hunt in order to retrieve the required material.
Objective: Slay Bulettes
From your current location, drive to the quest’s location, which should be south of Lestallum.
The Bulettes you have to slay will spawn during the day at the bottom of an antenna tower, inside a small yard.
If you encounter difficulties when you fight these beasts, try using Shields, Machineries and Ice spells. All of them will deal 120% damage to the Bulettes in FFXV.
Avoid using Fire spells and Light spells, because they will inflict only 50% damage.
Blocking their frontal attacks is the key to winning this battle. If you run out of MP, take cover behind the buildings in the courtyard.
Your goal, is to retrieve at least one Bulette Carapace by the end of this encounter. If the material doesn’t drop, you can rest at the camp nearby and fight the beasts again.
Objective: Deliver the Bulette Carapace to the Arms Merchant
When the Bulette Carapace finally drops, fast travel to your car and then drive back to the quest giver.
In exchange for bringing him the Bulette Carapace, you will receive the rewards listed below and you will unlock the Tails Spin side quest.
Ace of Carapace Quest Info
Description: “The arms merchant will compensate Noctis for bringing him the carapace of the shielded monster known as bulette.”
Reward: Discount to all items sold by this vendor
Post Quest Suggestion
Complete Tails Spin side-quest.