The present work proposes a combined experimental methodology and optimization strategy of the process parameters for the turning of Nimonic C-263 superalloy with a multilayer CVD coating using TiN-MT-TiCN-Al2O3 grade KCM25 inserts. Taguchi's L-27 orthogonal array is used for the experimental design. The outcomes of machining parameters viz. cutting speed (vc), cutting feed (f), depth of cut (ap), cryogenic temperature (T) and holding time (t) are explored on the machining characteristics like surface roughness (SR), nose wear (NW), flank wear (NW) and cutting force (F). The results are further compared with the cryogenic environmental studies that have improved the tool life and led to better machinability of the alloy. The multiple responses of the cryogenic machining environment are converted into the equivalent closeness factor (CF) using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. The TOPSIS based results are further improved using a neuro-genetic algorithm (combined ANN-GA). A confirmatory test is further carried out on the optimum machining parameters obtained by the hybrid approach (the combination of TOPSIS and ANN-GA) to validate the proposed work. It is seen that the closeness factor is improved by 6.17 %. The proposed model can be useful to select the ideal process conditions and to enhance the productivity of turning processes. © 2020 The Society of Manufacturing Engineers