This is a personality type usually described by the words "prima donna". Here's the definition from Wikipedia:
Sometimes, these "prime donne" (the Italian plural form) were grand with their off-stage personalities, and demands on fellow troupe members, musicians, set and wardrobe designers, producers and other staff but were deferentially tolerated because of their commensurate talent and "pulling power", that is, their draw at the box office. From this experience, the term "prima donna" has come into common usage in any field denoting someone who behaves in demanding, often temperamental, fashion revealing an inflated view of themselves, their talent, and their importance. [4] Due to this association, the contemporary meaning of the word has taken on this negative reference.
Today the term has become a mainstream word outside of opera to often describe a vain, undisciplined, egotistical, obnoxious or temperamental person who finds it difficult to work under direction or as part of a team, and although irritating, cannot be done without.
Most businesses have them at one time or another - we've had some classics. I would have to describe some bosses that way too.
