"Shaping up well" means what these other tutors have described: progressing nicely. It often, however, is used to describe a person. For example:
"When John was really little, he was always in trouble for talking back and biting his brother. Since moving him to an alternative program, John's behavior has gotten a lot better. He is really shaping up well in time for admission into the private elementary school."
If it is used to describe something other than a person, it is often about a project or process.
"It started off messy, but my ceramics project is finally shaping up well."