As an entrepreneur you can attain any level of education you want. There are tons of examples successful entrepreneurs that don’t have any formal education. The one thing all successful entrepreneurs have in common is there ability to identify a problem and find a creative and unique solution to that problem.
As others have said, you can reach any level of education that you desire. However, a Masters in Business Administration is typical for an entrepreneur. Undergraduate studies in whatever field you want to be an entrepreneur in (music, sports medicine, software, etc) and then a masters in business will give you the tools you need to get businesspeople to listen to you and, more importantly, invest in you. You'll learn how to create business plans and talk to investors, read markets and make pitches.