This Royal Duo are typical Draenor Sproutlings that pack a BIG PUNCH!
I admit, I did think initially that a couple of water attacks would do it, but their hits can be really huge, especially once Righteous Inspiration goes out (and they do a bit of Righteous Inspiration trading between the two of them). I had tried the Pandaren Water Spirit + Chrominius combo but I couldn't quite get that to work, then I tried some magic pets so that I wouldn't get 1 hit with an Inspired attack, but that didn't quite work for me either and and went another tack.
These are their attacks:
The team I beat with consisted of Ruby Droplet and a S/S Death Adder Hatchling. I had another pet in the team but it never got used.
I started with Acid Touch, and then used Bubble and then Drain Blood. That got my health back up by about 750 and by that stage they had used Righteous Inspiration and the Inspired attack was still blocked by bubble. I then switched to Death Adder Hatchling and Blinding Poison, then followed that with Puncture Wound and then used Poison Fang and then switched back to Ruby Droplet, who fortunately still had a block up and the next attack was blocked and I put another Acid Touch, followed with Bubble and the Drain Blood again. By this time one of the royal duo had died and I applied another Acid Touch to the other and switched back to my Death Adder Hatchling and Blinding Poison, Puncture wound and then Poison Fang and they royal pair were defeated! Fortunately for me, the Floret had used a Righteous Inspiration when I applied Blinding Poison so I was not killed with the next hit - phew!
The beauty of the Garrison pet battle daily is that I can try it again - but I still couldn't get success with my Pandaren water spirit and Chrominius. I look forward to reading other people's strats and trying them out!