Transformers potential failure sources can be summerized as below main causes. Especially #3, 4, 5 with high criticality.
Bushings
Insulation deterioration
Short circuit
Mechanical damage
On-Load Tap Changer (OLTc)
Internal Arc
Mechanical damage
Windings
Stress due to Internal failures
Mechanical damage
Core
Improper insulation
Excessive Heating
Loose laminations/stacking
Oil
Oxidation of the oil
Thermal decomposition
Moisture contamination