Despite the remarkable advances in deep learning-based voice conversion systems, the misalignment between the training objective function and perceptual evaluation metrics remains one of the main obstacles to improving output quality. On the other hand, this field requires more objective and standardized metrics for comprehensively evaluating its performance. In GAN-based non-parallel voice conversion systems, particularly in the CycleGAN-VC family and including MaskCycleGAN-VC, discriminators are typically trained to distinguish between real and fake data and are not directly aligned with metrics such as mel-cepstral distance, intelligibility, speaker similarity, or the naturalness of speech. This paper presents a method called MetricCycleGAN-VC, which, by modifying the secondary discriminators and adding a continuous output, enables learning the behavior of evaluation metrics in the form of a black-box strategy. In this framework, the metrics MoMCD, STOI, SECS, MoNISQA, along with the image-based metrics FSIM, SSIM, and GMSD, are employed to guide training. Evaluations were conducted on the VCC2018 dataset across four gender conversion settings, including female-to-female, female-to-male, male-to-female, and male-to-male. The results show that applying each metric during training primarily improves that same metric in the output. Additionally, among the image-based metrics, GMSD was able to achieve a simultaneous and harmonious improvement across all four evaluation indicators. Subjective listening assessment also confirms the superiority of the proposed method over MaskCycleGAN-VC.