Is a personal training certification sufficient to establish your own business? Is a college degree needed?
Establishing your own business is regulated at state level, and you need to make sure that you educate yourself on those requirements. This process is independent of any certification or degree here in North Carolina, and I am pretty sure everywhere else.
You may investigate, though, about the legal form that your business should have. There are various forms from sole proprietorship to S-corporations for example, and I would advise that you make yourself knowledgeable what will be the best for your particular situation.