We theoretically investigate the sensing performance of the dielectric-metal core-shell resonators (DMCSRs) that support multipolar sharp magnetic and electric-based cavity plasmon resonances. We show that at the cavity resonances the ability of the DMCSRs to strongly confine the optical fields inside the cavity is robust against the existence of nano-openings in the metal shell layer. As a result, both the perfect DMCSRs having a complete metal shell layer and the non-perfect DMCSRs with nano-openings in the metal shell layers exhibit high refractive index sensitivities of 700 ~1200 nm/RIU. Furthermore, we demonstrate that such high refractive index sensitivities could be well maintained in an array of interconnected non-perfect DMCSRs. The narrow linewidths of the cavity plasmon resonances coupled with their high index sensitivities make the array of non-perfect DMCSRs possess high figure of merit (FOM) values up to ~88, approaching the theoretically estimated upper limit (FOM ≈108) for gold standard prism coupled surface-plasmon sensors.