As a World Boss, Brealeos appears in Lost Ark at regular intervals (every few days, at set periods of the day). Find this boss and give it a good beating until it drops the item you need to complete your set of Island Souls. You may be at a loss as to where this boss might be found and at what times if you have already searched every continent. The location of Brealeos in Lost Ark is detailed here for your convenience.

How to Track Down Brealeos, the World Leader's Boss in the Temple of the Lost Ark
There are spawning grounds for Brealeos on Frostfire Island, not far from Shushire. The island can be found by choosing the same grid location as Shushire's port. To make things simpler, a port icon has been conveniently placed near the top of the map in the vicinity of the area. Frostfire Island is located in the Cold Snaps Seas to the north of the harbor. To engage Brealeos, you'll need to sail to this location. Fortunately, you can visit the island whenever you like, and you can even designate it as a Bifrost location and Lost Ark gold for sale!

Every Lost Ark field boss appears at specific times and dates. Every few days, they repeat the same schedule they've established. View an example of the Brealeos field boss's alarm schedule in the image below.

Having the appropriate item level is also a requirement for engaging Brealeos in battle. The minimum required item level to aid in the fight when using Brealeos is 460. Even if you're below this level, you'll still be able to do some damage; however, it will be extremely difficult for you to earn contribution points.

Getting the Feeling of Reality When You're Not Soul of the Bamboo Islands
After you've gotten your item level high enough to join in, proceed to the dock in Shushire and sail north until you reach the island. You can get your ship fixed up at the harbor if it's worn out and you want to take it out for a spin again.