Clinical application of anticancer drugs is mostly limited due to their hydrophobic nature, which often results in lower bioavailability and lesser retention in systemic circulation. Despite extensive research on the development of targeted drug delivery systems for cancer treatment, delivery of hydrophobic therapeutic drugs to tumor cells remains a major challenge in the field. To address these concerns, we have precisely engineered a new hyperbranched polymer for the targeted delivery of hydrophobic drugs by using a malonic acid-based A2B monomer and 1,6-hexanediol. The choice of monomer systems in our design allows for the formation of higher molecular weight polymers with hydrophobic cavities for the efficient encapsulation of therapeutic drugs that exhibit poor water solubility. Using several experimental techniques such as NMR, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), Fourier transform-infrared (FT-IR), and gel permeation chromatography (GPC), the synthesized polymer was characterized, which indicated its dendritic structure, thermal stability, and amorphous nature, making it suitable as a drug delivery system. Following characterizations, theranostic nanoplatforms were formulated using a one-pot solvent diffusion method to coencapsulate hydrophobic drugs, BQU57 and doxorubicin. To achieve targeted delivery of loaded therapeutic drugs in A549 cancer cells, the surface of the polymeric nanoparticle was conjugated with folic acid. The therapeutic efficacy of the delivery system was determined by various cell-based in vitro experiments, including cytotoxicity, cell internalizations, reactive oxygen species (ROS), apoptosis, migration, and comet assays. Overall, findings from this study indicate that the synthesized dendritic polymer is a promising carrier for hydrophobic anticancer drugs with higher biocompatibility, stability, and therapeutic efficacy for applications in cancer therapy.