This study reports a combined experimental–numerical investigation of hydraulic-assisted single point incremental forming (HA-SPIF) to enhance thickness uniformity in truncated quadrilateral parts formed from AA1050 aluminum alloy sheets. A finite element model is established and validated using experiments on circular blanks of 220 mm diameter and 1.0 mm thickness, forming components with a 60° wall angle and a target height of 55 mm. Material anisotropy is characterized through uniaxial tensile tests along 0°, 45°, and 90° to the rolling direction, and direction-dependent Voce hardening laws are calibrated from true stress–strain data, with flow stresses of 69.0–82.6 MPa and anisotropy coefficients of 0.45–0.86. The validated model is first employed to assess the effect of material orientation on thickness distribution, revealing pronounced differences in thinning behavior. A subsequent parametric study examines the coupled influences of hydraulic pressure, tool feed rate, and vertical step size on thickness variation and minimum residual thickness. Hydraulic assistance is shown to effectively suppress localized thinning and significantly improve thickness homogeneity relative to conventional SPIF. The main contribution of this work is the integrated consideration of anisotropic Voce hardening and hydraulic support for a non-axisymmetric geometry, providing a reliable predictive framework and practical guidelines for thinning control in high-precision forming applications.