Background/Objectives: For hyperlipidemic patients with statin resistance, a fixed-dose combination of a non-statin drug such as ezetimibe (EZT) and bempedoic acid (BA) provides a significant benefit. Although both drugs exhibit poor aqueous solubility, the oral bioavailability of EZT is more critically limited by dissolution, whereas BA maintains adequate absorption due to its high intestinal permeability. With regard to the reference product, Nexlizet^® (180/10 mg), our study focused on developing a novel tablet with superior in vitro performance without incorporating sodium lauryl sulfate (SLS), as it may potentially alter BA absorption. Methods: The solid dispersion technique (co-precipitation) was applied using the Kollidon^® VA64 polymer, and the solid state was characterized through differential scanning colorimetry (DSC), X-ray powder diffraction (XRPD), and Fourier transform infrared spectroscopy (FTIR). The prepared solid dispersions (SDs) were formulated into film-coated tablets (FCTs) and were characterized physically and for drug performance, and an animal model study was also conducted. Results: The solid-state analysis of the optimized SD formula (S30) revealed reduced drug crystallinity with no drug–carrier chemical interaction. The optimized formula (F30), a film-coated tablet, successfully achieved comparative in vitro dissolution versus Nexlizet^® and passed the accelerated stability study. Furthermore, in vivo evaluation revealed that F30 significantly reduced serum total cholesterol (TC), triglycerides (TG), and low-density lipoprotein (LDL), with an increase in high-density lipoprotein (HDL), in an animal model. Conclusions: These findings confirm that the SD technique is an effective one-step approach to co-formulating both APIs, simplifying manufacturing processes and optimizing the batch size.