We use a parallel multi-objective genetic algorithm to drive a search and reconstruction spectroscopic analysis of plasma gradients in inertial confinement fusion (ICF) implosion cores. In previous work, we had shown that our serial multi-objective Genetic Algorithm was a good method to solve two-criteria X-ray spectroscopy diagnostics problems. However, this serial version was slow and we therefore could not incorporate better physics and more criteria to solve larger problems and handle larger data sets. In this paper, we develop and use a parallel multi-objective genetic algorithm based on a master-slave model to solve three criteria spectroscopic analysis problems. The algorithm works well in reconciling experimental observations with theoretical physics model parameters. In addition, theoretical analysis and experimental results on the parallelized version show good scalability with up to 150 processors. This reduces the time for running the GA from 9.6 hours to 5.9 minutes.