The elusive nature of Dark Matter (DM) remains a mystery far from being solved. A vast effort is dedicated to search for signatures of feeble DM interactions with Standard Model particles. In this work, we explore the signatures of axion DM boosted by interactions with Supernova neutrinos: Neutrino-Boosted Axion DM (νBADM). We focus on νBADM converting into photons in the Galactic magnetic field, generating a peculiar gamma-ray flux. This signal falls in the poorly explored MeV energy range, that will be probed by next generation gamma-ray missions. Once more, astrophysical searches might act as a probe of fundamental physics, unveiling the nature and properties of DM.