The 'affair' is believed to have lasted around 6 months.
Brenner has spoken about his 'relationship' with the dolphin and even described the whole thing graphically in a short documentary called Dolphin Love.
He also opened up about the abuse he suffered as a child, which lead to him being attracted to animals and even trying to have intercourse with the family dog... something that didn't end very well, unsurprisingly.
It's not for the faint of hearted, that's for damn sure.
Now, the exact length of this strange tryst varies depending on the account you read, but rest assured, Brenner says it definitely happened.
Why would he lie, I guess?
Brenner explained: "I started rubbing her along her back, working my way to her flukes - her tail.
"And as I was rubbing her and moving my hand towards her tail, Dolly was slowly rolling around her long axis."
Then there's a whole load of stuff that we'll not get into here regarding anatomy and the actual nuts and bolts of the process, as well as - helpfully - an animated illustration of the act itself.
Honestly, you'll be fine without it.
At the time of events, it was 1971 - this sort of thing wasn't illegal - and Brenner was working as a photographer, meaning he had ready access to the dolphin after hours.
He said she 'announced her intentions to me by positioning herself so I was rubbing against her'.
Brenner explained: "At first I discouraged her, I wasn't interested. After some time I thought 'if this was a woman would I come up with these rationalisations and excuses'?
"It was when the park was closing that we successfully eluded the male dolphin so we could spend some time alone."
Eventually Dolly - yes, that was the dolphin's name - was moved to another amusement park, and reportedly died nine months later.
Brenner believes the sea mammal committed suicide because of her loss.
Dolphins are known to voluntarily stop breathing when they are depressed, and this is what he thinks happened.
Brenner said: "I called it a relationship because that's what it was. When she died it made me feel terrible and I fell into a depression which lasted five years,"
Of course, this isn't behaviour that should be encouraged. In fact, it should be actively discouraged.
But, in the unlikely event that you're interested to learn more about it, you can watch the full movie above.