Does a dedicated crook with a psychological problem stop robbing banks? Does a serial killer stop their murder spree? Mo. It takes a really good law enforcement effort to stop them. And so with the Lying Benghazi Witch.
The term "paralegal" is actually pretty broad, and covers the spectrum from what is basically an office assistant all the way to someone who handles substantive legal work.
The more legal education you have, the better your chances of being hired, and the more interesting work you'll eventually end up doing. Generally, most large firms or corporations are going to want someone with at least an Assocaite's degree. If you already have an undergrad degree, many programs will allow you to transfer credits, and do what's effectively a 6-month or one-year program and get another undergrad degree.
As far as national certifications (CLA) or professional associations (NALA, etc.) those are mainly resume boosters. Local paralegal associations are good for networking, and finding job openings. National associations are good for continuing legal education (required in a few states) and general guidance.
I don't know about BU, but I know that Hesser College has a good paralegal progam based out of the Nashua and Salem (NH) campuses. NALA and the National Federation of Paralegals also list many programs on their websites.
Good luck, and feel free to write if you want any more info.