Averting Crises in Housing Assistance Act or the ACHA Act This bill creates a mechanism for the Department of Housing and Urban Development (HUD) to identify and rehabilitate public housing agency (PHA) properties that are failing and revises requirements for contracts between PHAs and HUD. After designating a property as failing based on its physical condition or residents' complaints, HUD must enter into an agreement with the PHA to establish an action plan to restore the property to good condition. HUD must require the PHA to notify the residents of the property of the timelines and deadlines established by the plan. HUD must also provide technical and other assistance to the PHA and must provide housing vouchers to tenants wishing to relocate during the rehabilitation process. Residents of a failing property may sue HUD for damages if the property is not restored to good condition within one year after the PHA establishes an action plan. Additionally, the bill allows a consortium of PHAs to enter into a single annual contributions contract (i.e., the contract under which HUD agrees to pay a PHA for housing assistance and administrative fees).