  Many correlated metallic materials are described by Landau Fermi-liquid
theory at low energies, but for Hund metals the Fermi-liquid coherence scale
$T_{\text{FL}}$ is found to be surprisingly small. In this Letter, we study the
simplest impurity model relevant for Hund metals, the three-channel
spin-orbital Kondo model, using the numerical renormalization group (NRG)
method and compute its global phase diagram. In this framework, $T_{\text{FL}}$
becomes arbitrarily small close to two new quantum critical points (QCPs) which
we identify by tuning the spin or spin-orbital Kondo couplings into the
ferromagnetic regimes. We find quantum phase transitions to a singular
Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase
shows frustrated behavior involving alternating overscreenings in spin and
orbital sectors, with universal power laws in the spin ($\omega^{-1/5}$),
orbital ($\omega^{1/5}$) and spin-orbital ($\omega^1$) dynamical
susceptibilities. These power laws, and the NRG eigenlevel spectra, can be
fully understood using conformal field theory arguments, which also clarify the
nature of the non-Fermi-liquid phase.
