Twelve novel neo-tanshinlactone–chalcone hybrid molecules were constructed through a versatile methodology involving the Horner–Wadsworth–Emmons (HWE) olefination of 4-formyl-2H-benzo [h]chromen-2-ones and phosphonic acid diethyl esters, as the key step, and evaluated for anticancer activity against a series of four breast cancers and their related cell lines, viz. MCF-7 (ER + ve), MDA-MB-231 (ER-ve), HeLa (cervical cancer), and Ishikawa (endometrial cancer). The title compounds showed excellent to moderate in vitro anti-cancer activity in a range of 6.8–19.2 µM (IC50). Compounds 30 (IC50 = 6.8 µM and MCF-7; IC50 = 8.5 µM and MDA-MB-231) and 31 (IC50 = 14.4 µM and MCF-7; IC50 = 15.7 µM and MDA-MB-231) exhibited the best activity with compound 30 showing more potent activity than the standard drug tamoxifen. Compound 30 demonstrated a strong binding affinity with tumor necrosis factor α (TNF-α) in molecular docking studies. This is significant because TNFα is linked to MCF-7 cancer cell lines, and it enhances luminal breast cancer cell proliferation by upregulating aromatase. Additionally, virtual ADMET studies confirmed that hybrid compounds 30 and 31 met Lipinski’s rule; displayed high bioavailability, excellent oral absorption, favorable albumin interactions, and strong penetration capabilities; and improved blood–brain barrier crossing. Based on the aforementioned results, compound 30 has been identified as a potential anti-breast cancer lead molecule.