The wide range of materials featuring unique properties has contributed to the constant growth of 3D-printed items nowadays. Polyhydroxyalkanoate (PHA) is a biosourced material that is gradually growing in additive manufacturing. 3D printed PHA was examined herein under dynamic mechanical analysis. The aim was to reveal the critical 3D printing settings affecting the response of this eco-friendly polymer on its rheology and under combined thermal and force loadings, producing valuable information for the enrichment of the available experimental data. Optimization was attempted with Taguchi L9 experimental design, with four control parameters: deposition speed, layer height, extrusion temperature, and extrusion width. The response metrics were the Flexural Storage Modulus, Dynamic Glass Transition Temperature, and Damping Factor at Dynamic Glass Transition Temperature. Two regression models were applied and compared to form reliable prediction equations, and a confirmation run verified the outcome. Optical microscopy evaluated the samples' microstructure and quality. Two controls were distinguished for their remarkable impact, namely, deposition speed and layer height. Flexural Storage Modulus increased ∼15% with optimized settings selection. The optimization significance is unequivocal, promoting the utilization of PHA in Additive Manufacturing, with the valuable information provided on the mechanical response of this nature-sourced polymer.