In this work, a multi-objective Hybrid Bald Eagle Search Simulated Annealing (Hybrid BESSA) parameter extraction technique for photovoltaic (PV) modules is discussed. First, the efficacy of the Hybrid BESSA was proved via testing on unimodal functions, multimodal functions, and fixed dimensional multimodal functions and the results were compared with the Bald Eagle Search (BES) and other recently proposed optimization techniques. Then, a multi-objective Hybrid Bald Eagle Search Simulated Annealing (Hybrid BESSA) parameter extraction technique was devised for photovoltaic (PV) module parameter extraction. The Hybrid BESSA parameter extraction technique was simulated and analyzed in the MATLAB/SIMULINK environment and in a practical experimental setup for the PV Module AS-M3607-S (G1 CELLS). It was found that the Hybrid BESSA possessed better exploration and exploitation capabilities as compared to the BES and other state-of-the-art techniques. It was found that the fitness function value derived by the Hybrid BESSA technique was less than that of the BES technique when tested under various weather conditions. The percentage error for open circuit voltage, output power, and short circuit current was lower when derived by the Hybrid BESSA in comparison with the BES technique. From the results obtained from modeling the PV Module AS-M3607-S (G1 CELLS) based on Hybrid BESSA-based extracted parameters and BES-based extracted parameters, it was seen that percentage improvement in the combined objective function for the condition of keeping irradiance fixed at 1000 W/m2 at a temperature varying from −30 °C, 0 °C, 25 °C, 30 °C, 50 °C, and 70 °C were 0.9%, 8.5%, 29.2%, 0.03%, 5.7%, and 0.5%, respectively. When the temperature was kept fixed at 250 °C and irradiance varied from 1000 W/m2, 800 W/m2, 600 W/m2, and 400 W/m2, the percentage improvement in combined objective function was found to be 0.5%, 8.1%, 0.5%, and 0.8%, respectively. By analyzing the simulation as well as the experimental results, it was established that the PV model parameter extraction method based on the Hybrid BESSA is more accurate than the BES technique. This analysis is based on a single-diode PV module. A double-diode PV module analysis still needs to be explored.