When we talk about credentials, we are referring to "official" types of actions that result in receiving a degree, or certificate of some sort. First, while having a degree in a relevant field (or several degrees) may help you develop needed training and learning skills, it's not required in order to hang out a shingle. Second, there are no even close to universally accepted certifications for trainers.
So in short, you don't HAVE to have any formal credentials to become a trainer. As with any profession, the fact that one can enter the profession doesn't mean that you will succeed, or even have the basic skills required.
Opinions vary about the value of formal education and credentials in terms of having a successful training career. Some people claim that such education is exceedingly valuable, while others (usually who have gone another route) suggest that there is little if any correlation between any one set of credentials, degrees, or credentials, and success in a training career.