The physical properties of the accretion flow and of the X-ray emitting plasma, in supermassive black holes accreting at extreme Eddington rates, are still very unclear. Here we present the analysis of simultaneous XMM-Newton and NuSTAR observations of the hyper-Eddington Seyfert 1 galaxy IRAS 04416+1215, carried out in 2020. The main goal of these observations is to investigate the properties of the X-ray corona, as well as the structure of the accretion flow and of the circumnuclear environment, in this regime of extreme accretion. IRAS 04416+1215 has one of the highest Eddington ratio ($lambda_{rm Edd}simeq 472$) in the local Universe. It shows an interesting spectral shape with the presence of multi-phase absorption structure composed of three phases, whose estimate of the minimum and maximum distances suggests two different interpretations, one consistent with the three X-ray winds being co-spatial, and possibly driven by magnetohydrodynamical processes, the other consistent with the multi-phase winds being also multi-scale. The X-ray spectrum of IRAS 04416+1215 also has a prominent soft excess component and a hard X-ray emission dominated by a reflection component. Moreover, our detailed spectral analysis shows that IRAS 04416+1215 has the lowest coronal temperature measured so far by NuSTAR ($kT_e=3-22$ keV, depending on the model). This is consistent with a hybrid coronal plasma, in which the primary continuum emission is driven by pair production due to high-energy tail of the energy distribution of non-thermal electrons.
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