This is Akiko Yano and a dolphin on the cover of her album from 1977 called "Iroha Ni Konpeitou." You can see the track listing here or buy a copy from Amazon Japan. There's lots of Akiko Yano videos at YouTube, but I didn't spot any that involved dolphin wrestling. Via this Cheesy Vinyl Flickr gallery.
And this isn't the only bizarre cover featuring a dolphin that I saw today. I present Robert Merle's "Day of the Dolphin"
The book is apparently a satire about a dolphin trained to sabotage a ship transporting the president of the US. Even better, it was a movie:
I couldn't find a video clip, but here's a Simpsons parody inspired by the film's name:
I found one copy of the book with this cover at eBay. There's several original Day of the Dolphin posters on sale for under $30 at Movieposters.com. And the dvd is $6.50 at Amazon.
*Previously: Whale in an iceberg.