Biodiesel has been established as a promising alternative fuel to petroleum diesel. This study offers a promising energy conversion platform to valorise high acidity waste cooking oil (WCO) into biodiesel in a single-step reaction via supercritical methanol. Carbon dioxide (CO2) has been used as a co-solvent in the reaction with a catalytic effect to enhance the production of biodiesel. This work provides an in-depth assessment of the yield of four fatty acids methyl esters (FAME) from their correspondent triglycerides and fatty acids. The effects of four independent process variables, i.e., methanol to oil (M:O) molar ratio, temperature, pressure, and time, have been investigated using Response Surface Methodology (RSM). Four quadratic models have been developed between process variables and the yield of FAMEs. The statistical validation of the predicted models has been performed using analysis of variance (ANOVA). Numerical optimisation has been employed to predict the optimal conditions for biodiesel production. The predicted optimal conditions are at 25:1 M:O molar ratio, 254.7 °C, 110 bar within 17 min resulting in 99.2%, 99.3%, 99.13%, and 99.05% of methyl-oleate, methyl-palmitate, methyl-linoleate, and methyl-stearate yields, respectively. The predicted optimum conditions have been validated experimentally.