The word 'diva' originally described headline singers of opera. The "stars" of the opera world. Nowadays the word is used to describe someone who thinks highly of themselves, and think that their own needs or wants is more important than others. "Throwing a fit" is to start a disproportionally angry argument over something.

So "throwing a diva fit" is to get mad about something solely because it is not how you'd prefer it to be, regardless of what others think.

A “diva” is generally used nowadays to mean someone who complains about everything. So a diva fit would be a diva throwing a fit. Basically the adult version of a tantrum.