The interaction of high-energy electrons and X-ray photons with soft 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 (FA$\mathrm{<mrow\; data-mjx-texclass="ORD">0.79</mrow>}$MA$\mathrm{<mrow\; data-mjx-texclass="ORD">0.16</mrow>}$Cs$\mathrm{<mrow\; data-mjx-texclass="ORD">0.05</mrow>}$)Pb(I$\mathrm{<mrow\; data-mjx-texclass="ORD">0.83</mrow>}$Br$\mathrm{<mrow\; data-mjx-texclass="ORD">0.17</mrow>}$)$3$ 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 PbBr$2$, appear as a crystalline degradation phase after fluences of ~200 e$-${\AA}$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$. These changes are concomitant with the formation of small PbI$2$ 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.