Background: Alzheimer’s disease and related dementias (ADRD) are progressive conditions. Family caregivers of patients, especially those caring for patients with ADRD exhibiting behavioral and psychological symptoms of dementia (BPSD), undergo significant physical and mental changes during long-term care. While most researchers have focused on the specific needs of family caregivers, the comprehensive understanding of these needs is limited. In this study, Alderfer’s existence, relatedness, and growth theory was used to develop an interview framework to systematically and comprehensively understand the needs of family caregivers of individuals with ADRD. Objective: The objective of this study was to understand family caregivers’ needs in coping with BPSD in individuals with ADRD, aiming to alleviate caregivers’ stress and promote their overall well-being. Methods: This study used a hermeneutic–phenomenological interview research design. Data were collected via remote conferences involving interviews with 17 participants selected via maximum variation sampling. The Colaizzi seven-step method was utilized, and the interview contents were analyzed using NVivo 12.0 software. Results: The needs of family caregivers in coping with the BPSD of individuals with ADRD could be summarized into three themes, namely existence needs, relatedness needs, and growth needs, and 10 sub-themes. Conclusions: The study findings provide new insights into the needs of family caregivers in coping with patients exhibiting BPSD. Family caregivers experience significant negative emotions, poor caregiving experiences, heavy caregiving burdens, and a desire for professional assistance and policy support.