Associate's degrees are not often sufficient to break into cybersecurity on their own. If you have some experience in tech already, are trying to break into IT (via a 2-year IT AS), or supplement them with relevant certifications, this may be an option.
Bachelor's degrees are common for cybersecurity workers that choose to go through college as their route into tech, especially in areas such as software security (via 4-year CS degrees). Having a Bachelor's can also help you advance once you're in the field, as some companies will not consider people for advanced or leadership positions without higher education.
Master's degrees are less common, though some people will choose a Master's when build off their Bachelor's degrees. This may be either due to a career change, when looking for specific research opportunities, etc. Some cybersecurity workers will go up to a Master's (or do a combined BS/MS) before entering the workforce, but this is not a strict requirement.
PhDs are very irregular for the cybersecurity field, and aren't recommended unless you have particular goals you want to accomplish in academia (such as research, teaching, etc.).
As a reminder, degrees are not required for working in cybersecurity, though can provide certain advancement or opportunities. Please do not take this single FAQ entry as an indication that you must get one of the above degrees.