The interaction of high-energy electrons and X-ray photons with beam-sensitive semiconductors such as halide perovskites is essential for the characterisation and understanding of these optoelectronic materials. Using nano-probe diffraction techniques, which can investigate physical properties on the nanoscale, we perform studies of the interaction of electron and X-ray radiation with state-of-the-art (FA0.79MA0.16Cs0.05)Pb(I0.83Br0.17)3 hybrid halide perovskite films (FA, formamidinium; MA, methylammonium). We track the changes in the local crystal structure as a function of fluence using scanning electron diffraction and synchrotron nano X-ray diffraction techniques. We identify perovskite grains from which additional reflections, corresponding to PbBr2, appear as a crystalline degradation phase after fluences of ~200 e-Å-2. These changes are concomitant with the formation of small PbI2 crystallites at the adjacent high-angle grain boundaries, with the formation of pinholes, and with a phase transition from tetragonal to cubic. A similar degradation pathway is caused by photon irradiation in nano-X-ray diffraction, suggesting common underlying mechanisms. Our approach explores the radiation limits of these materials and provides a description of the degradation pathways on the nanoscale. Addressing high-angle grain boundaries will be critical for the further improvement of halide polycrystalline film stability, especially for applications vulnerable to high-energy radiation such as space photovoltaics.