The undergraduate calculus you mentioned should only be one-dimensional calculus, which is only a small part of advanced mathematics. It is enough to learn from scratch in half a year, let alone review.
The great mathematician halmos once said, "The only way to learn mathematics is to do it." Therefore, the key to learning calculus (advanced mathematics) is to "do", not only to do exercises, but also to prove theorems and examples, so that everything can be understood. Why do you think the teacher is so familiar with the courses he teaches? It is because he has repeatedly "done" for several years and decades, and everything has become instinct.
I wish you success!