Accelerating Access to Critical Therapies for ALS Act This bill establishes grant programs to address neurodegenerative diseases, such as amyotrophic lateral sclerosis (also known as ALS or Lou Gehrig's disease), and contains other related provisions. The Department of Health and Human Services (HHS) shall award grants to eligible entities to facilitate patients' access to investigational drugs that diagnose or treat ALS. The Food and Drug Administration (FDA) shall award grants to public and private entities to cover the costs of research and development of drugs that diagnose or treat ALS and other severely debilitating neurodegenerative diseases. HHS shall also establish the Public-Private Partnership for Neurodegenerative Diseases between the National Institutes of Health, the FDA, and at least one eligible entity (generally, an institution of higher education or a nonprofit organization). The partnership shall support the development and regulatory review of drugs that address ALS and other rare neurodegenerative diseases. The FDA shall publish on its website a five-year action plan for fostering the development of drugs that improve or extend the lives of people living with rare neurodegenerative diseases.