Whisk calamansi juice and soy sauce together in a shallow bowl. Add milkfish and marinate in the refrigerator for 1 hour.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Saute onion slices until softened, about 5 minutes. Transfer onion slices to a plate.
Heat remaining 3 tablespoons oil in the same skillet. Remove milkfish from the marinade, reserving marinade, and fry until lightly browned, 3 to 5 minutes per side. Pour in reserved marinade and bring to a simmer. Adjust sauce consistency with water. Season with salt and pepper. Serve milkfish and sauce with the sauteed onion.