We study the quasiparticle properties of a dipolar impurity immersed in a two-dimensional dipolar bath. We use the ab initio diffusion Monte Carlo technique to determine the polaron energy, effective mass, and quasiparticle residue. We find that both the polaron energy and quasiparticle residue follow a universal behavior with respect to the polarization angle when properly scaled in terms of the scattering length. This trend is maintained over a wide range of values of the gas parameter, even in the highly correlated regime. Instead, the effective mass shows growing anisotropy as the tilting angle is increased, which is induced, mainly, by the anisotropy of the impurity-boson dipole-dipole interaction. Surprisingly, the effective mass is larger in the direction of minimum interparticle repulsion. Finally, we use our Monte Carlo results to check the accuracy of perturbative approaches and determine their range of validity in terms of the gas parameter.
