We report a joint experimental and theoretical high-pressure study of the structural and vibrational properties of tetradymite-like (R%3m) b-As2Te3. Two samples have been characterized by angle-dispersive synchrotron powder X-ray diffraction and Raman scattering measurements under hydrostatic conditions with the help of ab initio calculations. One sample was synthesized at high pressure and high-temperature conditions with a Paris-Edinburg cell and the other by the melt-quenching technique. Both b-As2Te3 samples show the same properties and exhibit two isostructural phase transitions of order higher than 2, i.e. of electronic origin, near 2.0(2) and 6.0(5) GPa that are compatible with the changes predicted by recent electronic band structure calculations. The first isostructural phase transition can be attributed to the topological quantum phase transition from a trivial insulator to a topological insulator, passing through a 3D Dirac topological semimetal. This topological transition, specific to b-As2Te3, is not observed in isostructural Te-based sesquichalcogenides a-Sb2Te3 and a-Bi2Te3 that are topological insulators at room conditions. The second isostructural phase transition is likely related to an insulator-metal transition. Additionally, we have observed two partially reversible first-order phase transitions in b-As2Te3 above 10 and 17 GPa. We have found a high anharmonic behavior of the two Raman-active modes with the lowest frequencies in b-As2Te3 that explains the already reported ultra-low lattice thermal conductivity of b-As2Te3. Moreover, we have studied the similarities of b-As2Te3 with a-Sb2Te3 and a-Bi2Te3 (two of the best thermoelectric materials), thus providing insights into the origin of the ultra-low lattice thermal conductivity values in these compounds related to unconventional chemical bonds present in these isostructural materials.