Many conditions can lead to fetal hydrops. The most significant contributing factor is the fetal homeostatic response to relative hypoxia. For a number of reasons, the fetus is more prone to the acccumulation of interstitial fluid. This can be triggered by hypoxia as the fetal circulation responds in an attempt to maintain oxygenation of the tissues.
From Pathophysiology of hydrops fetalis:
Hydrops fetalis occurs when the rate of interstitial fluid production
by capillary ultrafiltration exceeds the rate of interstitial fluid
return to the circulation via lymphatic vessels. Developmental
differences in the microcirculation and lymphatic system of the fetus,
as compared with mature subjects, renders the fetus susceptible to
interstitial fluid accumulation. These differences include greater
capillary permeability, more compliant interstitial compartment, and
greater influence of venous pressures on lymphatic return. The balance
between interstitial fluid production and removal is most commonly
disrupted as a consequence of homeostatic mechanisms serving to
preserve adequate systemic delivery of metabolic substrate when
cardiocirculatory function is impaired. The pathophysiology of two
conditions of impaired cardiocirculatory function, atrial tachycardia
and severe anemia, serve as examples of the mechanisms by which these
homeostatic mechanisms perturb the balance of interstitial fluid
Hydrops can be immune (as in this case, due to incompatibility of fetal and maternal blood) or non-immune (e.g. cardiac, infectious, chromosomal, metabolic or non-immune haematological problems). Non-immune causes are much more common.
Haemolytic disease of the newborn occurs when there is an immune incompatibility between fetal and maternal blood (usually due to Rhesus incompatibility). This leads to breakdown of fetal red blood cells (haemolysis) which results in anaemia. This means that there is a reduced ability to carry oxygen and nutrients to the tissues. The condition is also known as fetal erythroblastosis due to the large number of erythroblasts seen in later stages.
The anaemia leads to compensatory tachycardia and eventually a high-output cardiac failure (this can also happen in adults due to anaemia).
From the Wikipedia page on high-output cardiac failure:
High-output heart failure is a heart condition that occurs when the
cardiac output is higher than normal due to increased peripheral
demand. There is a circulatory overload which may lead to pulmonary
edema secondary to an elevated diastolic pressure in the left
ventricle. These individuals usually have a normal systolic function
but symptoms are those of heart failure. With time, this overload
causes systolic failure. Ultimately cardiac output can be reduced to
very low levels.
Compensatory erythrogenesis (red cell production) in the liver and spleen causes circulatory obstruction in the liver and portal hypertension.
These changes, coupled with the increased capillary permeability and tendency to accumulate interstitial fluid, gradually lead to the development of fetal hydrops.
There is a useful summary on fetal hydrops at perinatology.com.