(1) Background: Paralympic women athletes in their training process go through a series of interrelated stages which are parallel to their evolutionary development, during which a wide variety of psychological, social, and biological factors will have an impact. The purpose of this study was to analyze the factors influencing the sports training process of Spanish Paralympic women athletes (social, sporting, psychological, technical–tactical factors, physical condition, as well as barriers and facilitators) who had won at least one medal (gold, silver, or bronze) in the 21st century Paralympic Games (from Sydney 2000 to Tokyo 2020). (2) Methods: The research involved 28 Spanish Paralympic women athletes who had won at least one medal at a Paralympic Games in the 21st century. An interview of 54 questions grouped into 6 dimensions (sport context, social context, psychological, technical–tactical, physical fitness, and barriers and facilitators) was used. (3) Results: Coaches, as well as families, were essential in the sport development of Paralympic athletes. In addition, most women athletes recognized that psychological aspects were of vital importance, as well as working on technical–tactical aspects and physical fitness in an integrated way. Finally, the Paralympic women athletes highlighted that they had to face numerous barriers, mainly financial challenges and issues with visibility in the media. (4) Conclusions: Athletes consider it necessary to work with specialists to control emotions, increase motivation and self-confidence, as well as to reduce stress and anxiety and manage pressure. Finally, the training process and sporting performance of Paralympic women athletes are conditioned by several barriers, including economic, social, architectural, and disability barriers. These considerations can be taken into account by the technical teams working with Paralympic women athletes, as well as by the competent bodies, to improve the sports training process of these athletes.