Yes, having a high school diploma and working towards an Associate's degree would likely qualify you to apply for an assistant manager position at a retail store. Many retail assistant manager positions don't require a college degree, but they do value experience and leadership qualities. Your progress towards a degree would demonstrate your commitment to education and potential for growth.
However, the specific requirements will vary significantly depending on the retail store and its size. Some larger chains might prefer candidates with more experience or a completed degree, while smaller, independent stores might be more flexible. It's always best to check the specific job posting's requirements to see if you meet their criteria.