"We have a very good boss."
Translation:У нас очень хороший начальник.
Hm. We use "у нас есть", if we want to intoduce something, to present something, to say that we have this.
But if we don't point that we have the boss, and if we want only to describe it, we don't use "есть"
У нас есть дочь - we have a daughter, we point that there is a daughter that relates to us
У нас добрая дочь - we have a kind daughter - we don't point that we possess a daughter, we point that our daughter is kind, we describe her
I hope that helps!
Yeah, it was very tricky - I never would have guessed it if I hadn't gotten this marked wrong. I only remembered it pointed out that you don't use "есть" when it's something that you obviously have (like a voice)
So есть is more in the "ownership" side of the "have" spectrum, i guess...
"Начальника" is the genitive and the accusative cases of "начальник", and using either of them here makes no sense. If you meant to say "female boss", that would be "начальница".