The expression is "fare-thee-well", not "fare-the-well".
Personally, I have never head "back and belly". I have heard, "beat (someone) until (he's) black and blue."
As someone else said, there are also a number of vulgar expressions which mean to beat (someone) severely. One of them is "to beat the crap out of (someone)". Other, even more vulgar words can be substituted for "crap".