  We present a comprehensive study of neutrino shock acceleration in
core-collapse supernova (CCSN). The leading players are heavy leptonic
neutrinos, $\nu_{\mu}$ and $\nu_{\tau}$; 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
$\nu_{\mu}$ 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.
