very well vs first-rate

very well is not an adjective while first-rate is an adjective.

Word	Noun	Adjective	Verb	Adverb
very well	No	No	No	Yes
first-rate	No	Yes	No	Yes

As adverbs, very well and first-rate are synonyms defined as:

very well (adjective)	first-rate (adjective)
	of the highest quality

very well (adverb)	first-rate (adverb)
quite well	quite well
an expression of agreement normally occurring at the beginning of a sentence