In this study, we changed the etch parameters (gas mixing ratio, radio frequency [RF] power, direct current [DC]-bias voltage, and process pressure) and then monitored the effect on the $HfAlO_3$ thin film etch rate and the selectivity with $SiO_2$. A maximum etch rate of 108.7 nm/min was obtained in $Cl_2$ (3 sccm)/$BCl_3$ (4 sccm)/Ar (16 sccm) plasma. The etch selectivity of $HfAlO_3$ to $SiO_2$ reached 1.11. As the RF power and the DC-bias voltage increased, the etch rate of the $HfAlO_3$ thin film increased. As the process pressure increased, the etch rate of the $HfAlO_3$ thin films increased. The chemical state of the etched surfaces was investigated with X-ray photoelectron spectroscopy. According to the results, the etching of $HfAlO_3$ thin film follows the ion-assisted chemical etching.