Oh my goodness, why would anyone think that's a good idea? And what is this obsession with dolphins anyway?
Anyway, apart from the obvious danger of giving birth (=bleeding and possibly acting erratically) around wild animals, I'd be very worried about hygiene. So the dolphins might be perfectly nice to you but you're still in an environment with all sorts of dirt and micro-organisms floating about. So you're exposing your brand new baby to that and your open wound from the placenta. Why would you think that's a good idea?
I absolutely pro water birth and doing things "naturally". But just because it involves some part of nature, doesn't mean it's a "natural" thing for humans to do. And completely discounting even basic medical knowledge, like eg knowledge about hygiene, is just plain reckless.