<p>The present manuscript investigates the quantum parameter estimation (PE) of a two-level atom undergoing circular acceleration in a Minkowski spacetime with a reflecting boundary, interacting with a bath of fluctuating massless scalar fields. Employing the open quantum systems framework, we calculate the quantum Fisher information (QFI) to assess the precision of PE under the influence of acceleration and boundary effects. Our findings reveal that the reflecting boundary significantly enhances the QFI when the atom is in close proximity to the boundary, effectively mitigating decoherence, particularly at higher accelerations. In contrast, without the boundary, QFI decays rapidly with increasing acceleration. These results highlight the critical role of boundary conditions and acceleration in preserving QFI, offering valuable insights for advancing quantum metrology in relativistic and confined systems.</p>