It is important to note that "The Boston Accent" as commonly seen/heard in movies

1. largely never existed.
2. The version that did exist was much softer than media makes it seem
3. It also largely doesn't exist any more, because it was mostly a working-class accent and working-class people pretty much don't live in Boston any more. In addition, Boston is a pretty metropolitan city; the regional accents of the US have been dying out for decades

Amusingly, I am from Boston, despite my flair, and lived there for several years before moving away as a kid. I don't have the accent