score:11
There are two contemporary accounts of those festivities - "Langham letter" and "The Princely Pleasures at the Courte at Kenelwoorth". These have a certain discrepancy in how they describe this particular episode, but none of them mentions the dolphin being underwater, or it being an automaton. Here's how the author of "Princely Pleasures" describes the event:
From thence her Majestie passing yet further on the brydge, Protheus appeared, sitting on a dolphyn’s back. And the dolphyn was conveyed upon a boate, so that the owers seemed to be his fynnes. Within the which dolphyn a consort of musicke was secretly placed, the which sounded: and Protheus, clearing his voyce, sang this song of congratulation [...]
Thus, it seems the dolphin was simply a boat decorated to look like a marine animal, and Greenblatt added a bit of embellishment to the event in his book.
You can find an article comparing the two accounts here.