So after reading Cursed Child I was beyond excited for this character and I thought I'd share why. That said there are probably gonna be spoilers in here.

First and foremost, right off the bat I figured I'd like her because Bellatrix is her mom. To be honest out of all of my favorite characters I figured that Bella would be the least likely to have a baby but here she is lol. So she gets points just for being Bellatrix's daughter. xP Carry on her legacy well Delphi. :'D

Secondly I love her name. My friend and I, in the last 24 hours have made so many jokes about Bellatrix going 'derp, this is dolphin*. "Time to carry on the Black tradition, shame my mother, and ruin my kid's social life all at once." In all seriousness, as it has been pointed out, Delphi's name really refers to the oracle and I love her name's deeper more symbolic meaning. That alone is already setting up for a cool character.

I also really love her edgy af character design lol. The wing tattoo is badass and I adore her hair. Not because I had my hair dyed the same way for a while or anything... 0:D

Getting into her personality, I think that she's really cute and funny too. At least in the beginning when she was pretending to be a good guy. No less I loved how the first thing she did was jokingly try to mug Albus. It was one of those moments where I was like 'yup she's Bella's alright.' And (even though it was fake) I thought her mini-Albus crush was cute in that 'kid who has a crush on his babysitter' kind of way.

Of course I loved her more cunning personality towards the end too.She actually proved to be really smart if I do say so; I thought it was really clever of her to try to stop Voldy from killing Harry rather than trying to actually kill Harry herself. And the fact that she was able to play Albus and Scorpius so well was impressive. Like she ended up being so badass. Especially when she started flinging around Crucios then I was really like, 'yup, totally Bella's, just like her mum :'D'

I also think that she (given only one book of development) is a deep and compelling character. I mean she, like her mom, isn't exactly all there either but in a more subtle way. It's her delusions of grandeur that had me intrigued; when she stated that she was the past and present and was the future this world needed. That really struck me as interesting. Combine that with the above paragraph and I just think she's a really fascinating character.
In other words, despite my jokes about her being like Ebony from My Immortal, she's not a Mary Sue. And despite what the leak made it sound like (and more jokes) she isn't some edge lord, OC-like character. She was written just as well as all of the others.

Finally I have a lot of sympathy for her as well. Though she may have played it up a bit I do feel bad that she missed out on Hogwarts because of her heritage. And I do feel bad that (despite my love of Bellatrix) that her parents just abandoned her and then died. Because at the end of the day even though she had secondary motives, I do think that she just wanted to be with her father and wanted his love even though he'd never be able to love her. Again she's just like her mom except she longed for familial love where Bellatrix desired romantic love.

In conclusion, 10/10; Bellatrix spawned a great child. Though I would love to know how no one noticed that she was pregnant in the first place lol. Oh well, Dolphin is a great character so kudos to Rowling for impressing me again and satisfying my needs as a Bella fan and a Bellamort fan. And by all means extra kudos because Dolphin is still alive!