Lepidium peruvianum—an edible herbaceous biennial plant distributed in the Andes—has been used for centuries as food and as a natural medicine in treating hormonal disorders, as an antidepressant, and as an anti-osteoporotic agent. The presented study aims to prove its beneficial cosmetic and chemopreventive properties by testing the antiradical, whitening, cytotoxic, and anticancer properties of differently colored phenotypes that were extracted using three solvents: methanol, water, and chloroform, with the help of the chemometric approach to provide evidence on the impact of single glucosinolanes (seven identified compounds in the HPLC-ESI-QTOF-MS/MS analysis) on the biological activity of the total extracts. The tested extracts exhibited moderate antiradical activity, with the methanolic extract from yellow and grey maca phenotypes scavenging 49.9 ± 8.96% and 48.8% ± 0.44% of DPPH radical solution at a concentration of 1 mg/mL, respectively. Grey maca was the most active tyrosinase inhibitor, with 72.86 ± 3.42% of the enzyme activity calculated for the water extract and 75.66 ± 6.21% for the chloroform extract. The studies in cells showed no cytotoxicity towards the human keratinocyte line HaCaT in all studied extracts and a marked inhibition of cell viability towards the G361 melanoma cell line, which the presence of pent-4-enylglucosinolate, glucotropaeolin, and glucoalyssin in the samples could have caused. Given all biological activity tests combined, the three mentioned compounds were shown to be the most significant positive contributors to the results obtained, and the grey maca water extract was found to be the best source of the former compound among the tested samples.