(1) Background: Melanoma is an aggressive neoplasm derived from melanocyte precursors with a high metastatic potential. Responses to chemotherapy and immunotherapy for melanoma remain weak, underlining the urgent need to develop new therapeutic strategies for the treatment of melanoma. (2) Methods: The viability of NHDF and A375 cell cultures after the administration of the tested isoxazole derivatives was assessed after 24-h and 48-h incubation periods with the test compounds in the MTT test. ROS and NO scavenging analyses, a glycoprotein-P activity analysis, a migration assay, a test of apoptosis, and a multiple-criteria decision analysis were also performed. (3) Results: All compounds that were tested resulted in a slower migration of melanoma neoplastic cells. The mechanism of the antitumor activity of the tested compounds was confirmed-i.e., the pro-apoptotic activity of the compounds in A375 cell cultures. Compound O7K qualified for further research. (4) Conclusions: All the tested compounds inhibited the formation of melanoma metastases and demonstrated the ability to reduce the risk of developing drug resistance in the tumor. The MCDA results showed that O7K showed the strongest antitumor activity.