Dear S____:

You wrote:

>>Would it be possible for you to tell me whether or not this sentence is grammatically correct.

>>”Well done; you’ve a healthy and balanced approach to life.”

>>Should it not read-“Well done, you have a healthy and balanced approach to life.”

The first is correct. This is really two sentences or clauses. The first is elliptical, but the “you have” or “it is” is understood. That is the way we often respond to what others say or do.

Example:
“What is your name?”
“James.” (i.e., “My name is James.”)

So it is with the expression “well done.”

I hope this helps.