This research employs the Taguchi method and analysis of variance (ANOVA) to investigate, analyze, and optimize the impact strength of tough polylactic acid (PLA) material produced through fused deposition modeling (FDM). This study explores the effect of key printing parameters—specifically, infill density, raster angle, layer height, and print speed—on Charpy impact strength. Utilizing a Taguchi L16 orthogonal array experimental design, the parameters are varied within defined ranges. The results, analyzed through signal-to-noise (S/N) ratios and ANOVA, reveal that infill density has the most substantial impact on Charpy impact strength, followed by print speed, layer height, and raster angle. ANOVA identifies infill density and print speed as the most influential factors, contributing 38.93% and 36.51%, respectively. A regression model was formulated and this model predicted the impact strength with high accuracy (R2 = 98.16%). The optimized parameter set obtained through the Taguchi method, namely, a 100% infill density, 45/−45° raster angle, 0.25 mm layer height, and 75 mm/s print speed, enhances the impact strength by 1.39% compared to the experimental design, resulting in an impact strength of 38.54 kJ/m2. Validation experiments confirmed the effectiveness of the optimized parameters.