No, you definitely do not need certification from anyone to be a shopper. Many companies will "certify" you for doing shops for various clients--whether they call it a 'certification' or 'training' or 'briefing' etc. Those qualifying tests/quizzes do not cost you any money and some companies even test you before you can complete your registration to become activated with them.
You will read a lot of discussion about the usefulness of MSPA certifications. Some shoppers in areas with many competitors feel that the paid certifications have been useful to them. Most of keep our $ in our pocket and do quite well without certification. Only a handful of companies actually use the MSPA certification and they are generally the SASSIE reporting system companies that support the MSPA. Better jobs are generally available elsewhere anyway. Do not be misled that the MSPA is a shopper's organization. It is a professional organization of the companies that hire us and they will not assist you in a dispute with a company regarding pay or anything else.