Mountain arnica Arnica montana L. is a source of several metabolite classes with diverse biological activities. The chemical composition of essential oil and its major volatile components in arnica may vary depending on the geographical region, environmental factors, and plant organ. The objective of this study was to characterize the chemical composition of essential oil derived from A. montana achenes and to investigate its effect on induction of apoptosis and autophagy in human anaplastic astrocytoma MOGGCCM and glioblastoma multiforme T98G cell lines. The chemical composition of essential oil extracted from the achenes was examined with the use of Gas Chromatography–Mass Spectrometry GC-MS. Only 16 components of the essential oil obtained from the achenes of 3-year-old plants and 18 components in the essential oil obtained from the achenes of 4-year-old plants constituted ca. 94.14% and 96.38% of the total EO content, respectively. The main components in the EO from the arnica achenes were 2,5-dimethoxy-p-cymene (39.54 and 44.65%), cumene (13.24 and 10.71%), thymol methyl ether (8.66 and 8.63%), 2,6-diisopropylanisole (8.55 and 8.41%), decanal (7.31 and 6.28%), and 1,2,2,3-tetramethylcyclopent-3-enol (4.33 and 2.94%) in the 3- and 4-year-old plants, respectively. The essential oils were found to exert an anticancer effect by induction of cell death in anaplastic astrocytoma and glioblastoma multiforme cells. The induction of apoptosis at a level of 25.7–32.7% facilitates the use of this secondary metabolite in further studies focused on the development of glioma therapy in the future. Probably, this component plays a key role in the anticancer activity against the MOGGCCM and T98G cell lines. The present study is the first report on the composition and anticancer activities of essential oil from A. montana achenes, and further studies are required to explore its potential for future medicinal purposes.