Laser-induced breakdown spectroscopy (LIBS) and principal component analysis (PCA) are frequently used for analytical purposes in research and industry, but they seldom are part of the chemistry curriculum or laboratory exercises. This case study paper describes the combined application of LIBS and PCA during a research internship for an undergraduate student. The instructional method applied was based on a one-on-one mentorship, in which case the learner was engaged in a research work. The learning activities included theoretical introductions to the LIBS and PCA methods, numerical simulation, experiments, and data analysis. The study covered three main topics: analysis of LIBS spectra, application of PCA for clustering, and use of PCA for experimental design. The realization of the study was instructive for all parties involved: from the mentorship point of view, it is concluded that the topics can be covered during an internship or developed into a one semester long research-based module of a chemistry program or a final year project. The student, on the other hand, developed profound technical skills in performing experiments and using PCA software for data analysis.