Natural Deep Eutectic Solvents (NADES) are eco-friendly solvents with considerable potential for extracting bioactive compounds. In this study, we aimed to extract phenolic compounds from Hass avocado residues (epicarp and seed) using NADES in combination with ultrasound-assisted extraction (UAE) and pressurized liquid extraction (PLE) as advanced processes. Ten eutectic mixtures, consisting of choline chloride (ChCl) or betaine as HBA (hydrogen bond acceptors), as well as fructose (Fru), glucose, lactic acid (Lac), citric acid, or glycerol as HBD (hydrogen bond donors), were prepared through stirring and heating. The estimated values for total phenol content (TPC), proanthocyanidin content (PAC), monomeric anthocyanin content (MAC), and antioxidant capacity of the extracts demonstrated a noticeable influence of these solvents. The PLE process significantly enhanced the extraction of phenolic compounds from the epicarp, as evidenced by TPC (185 ± 9 mg gallic acid equivalent/g dry sample) and PAC (77.8 ± 6 mg proanthocyanidin B2/g dry sample) values. Phytochemical characterization conducted via HPLC-QTOF-MS/MS revealed the great extraction power of ChCl:Fru and ChCl:Lac, and the improvement of extraction efficiency through PLE. These results imply that the synergistic use of innovative solvents and advanced processes, especially under high pressures, offers a sustainable approach for recovering phenolic-rich by-products such as avocado residues.