This study is based on the design and numerical investigation of a high-accuracy plasmonic biosensor. A dual-core Photonic Crystal Fiber (PCF) has been designed to obtain superior characteristics to its kindred. As for the plasmonic layer, a thin layer of titanium dioxide over a layer of gold has been used both of which contribute to the occurrence of Surface Plasmon Resonance (SPR). Circular airholes positioned in a rectangular manner pave the way to light entrapment. A Perfectly Matched layer (PML) is placed to help absorb the reflected light. The analysis of this structure’s performance was carried out considering the wavelength and amplitude sensitivity, the figure of merit (FOM), and the sensor resolution. The values go as fine as 22,000 nm/RIU for wavelength sensitivity, 3446 RIU⁻¹ for amplitude sensitivity, and 4.54 × 10⁻⁶ for the sensor’s resolution. Also, the maximum FOM found is 241.76 RIU⁻¹. The proposed structure, where the external sensing technique is used, shows excellent micro-scale sensing properties. To achieve such attributes, different structural parameters like pitch, gold and TiO₂ thickness, and air-hole diameters were altered. Keeping in mind the feasibility of fabrication, the design was kept simple while balancing the optimum properties.