After accepting this quest, we can take the elevator back upstairs. Once upstairs, head in the direction opposite the Self-Destruct Brute; there's a path over here.
When you see the person and the stairs ahead, don't go up the stairs yet; turn right instead.
There's some Dust to pick up below.
After picking it up, head up the stairs. Three Bronze Statues will spawn in front of us. Defeat them to obtain "Black Stone Fragment #4." Here, we can assemble a complete Black Stone to gain stat boosts.

