Absolutely, if it is referencing you as both a person and a professional.
If someone says "Joe Bloggs is a terrible developer and you should never hire him" on Twitter then it is very possible that when someone Google's "Joe Bloggs developer bristol" they will see that statement on Twitter.
It's often said that employers Google people they are about to hire. I've hired a developer before and I can say that one of the first things I do is Google the name and see what they have done. At my first employer we turned a fairly decent developer away because of what we found from a Google search (and the posting of NSFW content during work hours).
Absolutely, and a good lawyer can cost a fair bit of money. However, if it is in the interests of your professional life then it is worth the investment.
Besides, after a few hours consultation with a lawyer the most you'll probably see is a concise letter written by your lawyer to the offending party and the immediate retraction of any offending material online. Legal threats make even the most legal savvy of us jump out of our skins and bend to the will of the request.