I’m a machine learning engineer who came from a business background. Here are my two cents on your issue:
First, it is possible to get into machine learning without a Master’s or Ph.D. in the field.
But you will need a credible substitute for the degree to prove that you have the skills. Self-study alone is usually not sufficient.
I suggest you look for data analyst positions in companies that also have needs for machine learning/data science. The bar is much lower for a data analyst. You might start out doing Excel analysis. But you can learn machine learning in your free time and then gradually look for opportunities to use your modeling skills in your data analysis work. If you do a good job, you’ll have a good shot at transferring into a machine learning position because the company already knows you, and your work is evidence that you know your stuff.
The skills you should initially focus on are Python programming, SQL/databases, and statistics, and math.
I see the math concerns you especially. It doesn’t have to. I’ve written a series of blog posts on statistics, linear algebra, and calculus required for machine learning (the forum doesn’t allow me to post more than two links, but you’ll find the last topic easily if follow the first two).
If you read through the posts and understand the topics, you have a very good foundation for applied machine learning. No need to take years of advanced calculus in university.
Next, study sci-kit learn, and perhaps a Deep Learning framework like TensorFlow.
Once you’ve got this under the belt, you are in a good position to tackle some personal projects. Head over to Kaggle, download a dataset that interests you and start applying your models.
The next step is professional projects and you are on your way to being a full-fledged machine learning engineer.