We present a comprehensive study of neutrino shock acceleration in core-collapse supernova (CCSN). The leading players are heavy leptonic neutrinos, $ u_{mu}$ and $ u_{tau}$; the former and latter potentially gain the energy up to $sim 100$ MeV and $sim 200$ MeV, respectively, through the shock acceleration. Demonstrating the neutrino shock acceleration by Monte Carlo neutrino transport, we make a statement that it commonly occurs in the early post bounce phase ($lesssim 50$ ms after bounce) for all massive stellar collapse experiencing nuclear bounce and would reoccur in the late phase ($gtrsim 100$ ms) for failed CCSNe. This opens up a new possibility to detect high energy neutrinos by terrestrial detectors from Galactic CCSNe; hence, we estimate the event counts for Hyper(Super)-Kamiokande, DUNE, and JUNO. We find that the event count with the energy of $gtrsim 80$ MeV is a few orders of magnitude higher than that of the thermal neutrinos regardless of the detectors, and muon production may also happen in these detectors by $ u_{mu}$ with the energy of $gtrsim 100$ MeV. The neutrino signals provide a precious information on deciphering the inner dynamics of CCSN and placing a constraint on the physics of neutrino oscillation; indeed, the detection of the high energy neutrinos through charged current reaction channels will be a smoking gun evidence of neutrino flavor conversion.
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