Many university libraries keep a copy of the solution manual on reserve. You cannot check it out, but you can photocopy (or scan) the chapters you need for free.
These platforms have verified solutions for the 8th edition. While they require a subscription, they offer step-by-step explanations (not just final answers) and are legal. You can usually get a 7-day free trial.
Muchas universidades tienen licencias de Libros de Oxford. Busca en la base de datos de tu biblioteca "Atkins Physical Chemistry 8th edition solutions".