What is the word to describe an advanced vocabulary?

Solution 1:

Most of the time, "plain" words have synonyms that sound more sophisticated or advanced. These synonyms are usually obscure and sometimes difficult to understand. Certain dictionaries, Google's in particular, will classify them as archaic, meaning the word is dated, rare, meaning the word is uncommonly used, or literary, meaning the word is almost always used in writing and literature rather than speech and everyday use.

Otherwise, these words are known by a very wide variety of terms, the most common being the first and third you mentioned: advanced and academic vocabulary. I have also heard this broad category referred to as "high-leveled", "sophisticated", and "intellectual".

Solution 2:

Florid is a great one.

Florid: (of language) using unusual words or complicated rhetorical constructions. [Oxford Dictionaries]

Solution 3:

The closest adjective I found is ornate:

1.1(Of literary style) using unusual words and complex constructions. [Lexico]