  We report ultra-strong high-order nonlinear multiphoton processes in
monolayer MoS$_2$ (1L-MoS$_2$): the third harmonic is thirty times stronger
than the second harmonic, and the fourth harmonic is comparable to the second
harmonic. We find that second and third harmonic processes are strongly
dependent on elliptical polarization, which can be used to selectively tune
harmonic generation with different orders. We explain this by calculating the
nonlinear response functions of 1L-MoS$_2$ with a continuum-model Hamiltonian
and quantum-mechanical diagrammatic perturbation theory, highlighting the
crucial role of trigonal warping. A similar effect is expected for all other
transition-metal dichalcogenides. Our results pave the way for efficient and
tunable harmonic generation based on layered materials for various
applications, including microscopy and imaging
