Slice pork belly into 1-inch pieces layered with skin, fat, and meat.
Heat sugar in a large wok or pot over medium heat until it melts and caramelizes into a light brown syrup, about 5 minutes. Add pork and increase heat to high. Cook and stir to render some of the pork fat, 3 to 5 minutes.
Stir shallots and garlic into the wok. Add fish sauce and black pepper; stir to evenly coat pork. Pour in coconut water and bring to a boil. Add eggs, reduce heat to low, and simmer, covered, until pork is tender, about 1 hour.
Remove wok from the heat and let stand, about 10 minutes. Skim the fat from the surface of the dish.
