Thermal diodes--devices that allow heat to flow preferentially in one direction--are one of the key tools for the implementation of solid-state thermal circuits. These would find application in many fields of nanoscience, including cooling, energy harvesting, thermal isolation, radiation detection and quantum information, or in emerging fields such as phononics and coherent caloritronics. However, both in terms of phononic and electronic heat conduction (the latter being the focus of this work), their experimental realization remains very challenging. A highly efficient thermal diode should provide a difference of at least one order of magnitude between the heat current transmitted in the forward temperature (T) bias configuration (Jfw) and that generated with T-bias reversal (Jrev), leading to ℛ = Jfw/Jrev ≫ 1 or ≪ 1. So far, ℛ ≈ 1.07-1.4 has been reported in phononic devices, and ℛ ≈ 1.1 has been obtained with a quantum-dot electronic thermal rectifier at cryogenic temperatures. Here, we show that unprecedentedly high ratios of ℛ ≈ 140 can be achieved in a hybrid device combining normal metals tunnel-coupled to superconductors. Our approach provides a high-performance realization of a thermal diode for electronic heat current that could be successfully implemented in true low-temperature solid-state thermal circuits.