The etching mechanism of $ZrO_2$ thin films and etch selectivity over some materials in both $BCl_3$/Ar and $BCl_3/CHF_3$/Ar plasmas are investigated using a combination of experimental and modeling methods. To obtain the data on plasma composition and fluxes of active species, global (0-dimensional) plasma models are developed with Langmuir probe diagnostics data. In $BCl_3$/Ar plasma, changes in gas mixing ratio result in non-linear changes of both densities and fluxes for Cl, $BCl_2$, and ${BCl_2}^+$. In this work, it is shown that the non-monotonic behavior of the $ZrO_2$ etch rate as a function of the $BCl_3$/Ar mixing ratio could be related to the ion-assisted etch mechanism and the ion-flux-limited etch regime. The addition of up to 33% $CHF_3$ to the $BCl_3$-rich $BCl_3$Ar plasma does not influence the $ZrO_2$ etch rate, but it non-monotonically changes the etch rates of both Si and $SiO_2$. The last effect can probably be associated with the corresponding behavior of the F atom density.