Parastrephia quadrangularis (tola) is a native plant of the Chilean Andean Altiplano that is traditionally used for its anti-inflammatory properties. In this study, the aerial parts of the plant were analysed to determine their fatty acid (FA) profile and to identify bioactive compounds using gas chromatography–mass spectrometry (GC–MS). Both conventional extraction methods and Supercritical Fluid Extraction (SFE) were employed, using a 2³ factorial design with centre-point replicates. The variables included temperature (30–60 °C), pressure (15–45 MPa), and ethanol as a cosolvent (0–30% v/v). Extraction kinetics were evaluated using a linear spline model under central conditions (45 °C, 30 MPa, 15% ethanol). Response variables included extraction yield, Total Phenolic Content (TPC), antioxidant activity measured by Trolox Equivalent Antioxidant Capacity (TEAC), and FA composition. A factorial design identified pressure and ethanol concentration as key drivers of phenolic content and antioxidant activity, as supported by confocal autofluorescence microscopy. Multi-response optimisation based on the desirability function was applied to simultaneously maximise all response variables, yielding predicted optimal extraction conditions at 60 °C, 45 MPa, and 30% v/v ethanol for P. quadrangularis. The FA profile highlighted polyunsaturated FAs such as oleic, linoleic, and linolenic acids, as well as saturated FAs including palmitic and lignoceric acids, and short-chain non-volatile FAs. GC–MS analysis revealed metabolites potentially responsible for the plant’s traditionally reported therapeutic effects. Overall, these results highlight ethanol-based SFE as a sustainable strategy for recovering phenolic compounds and antioxidant-related fractions from ancestral medicinal plants.