A Better Drillbreaker - Hammerhead

First Available: Chapter 8
Other Requirements: Acquire Drill Breaker Item
Location: Hammerhead
Rewards: 2,000 EXP & Drillbreaker Plus

The item you need to start this quest is the Drill Breaker which you'll find in Formouth Garrison, one of the Imperial Bases in Leide (the desert portion of the map). If you'd like to see where on the map in Formouth Garrison the Drillbreaker is found, check my screenshot below. Once you have this item all you need to do is talk with Cid in Hammerhead to receive this quest.

For this quest Cid will ask you to bring him an item to upgrade the Drillbreaker with, in this case he'll ask you for a Magitek Core which you're able to acquire one of a few different ways. Each of the ways that I know of to acquire the Magitek Core are listed below.

Ways to Obtain Magitek Cores

1. Stealing the Past Quest
2. Costlemark Tower Menace Dungeon
3. Gralea and Insomnia (Chapter 13 & 14)
4. Pitioss Dungeon
5. Drop from MA-X Dux and MA-X Patria enemies

Drillbreaker Map Location in Formouth Garrison

Out of all the locations you can find the Magitek Core, the Stealing the Past is probably the easiest and most straight forward since you're guaranteed one and it's extremely easy to complete. All you need to do is loot a box outside of Pitioss Ruins and you'll both complete the quest and obtain the item we're after.

Magitek Core Outside Pitioss Obtained.