I completely forgot about the Lightning Round on my first run, so my first experience with it was in Hero Mode. It's tough, and took me a solid couple of hours to beat it. I always started with The Hoard since it's the most likely battle to inflict damage and there's less opportunity to be on the defensive. There's also a strategy I've read about that you can do before the challenge actually begins.. Go up to Skyloft and buy a guardian potion, upgrade it to the point of invincibility, and make sure you have your potion medal in your pouch to extend the effects. Go back down to the Gorge and drink the potion right before talking to the Thunder Dragon. The potion effect will carry into the challenge and last you the first few battles, you can get through the first few battles without losing any hearts.
Some people are really adamant that this method is "cheating". Personally, I disagree, It's not like you're taking advantage of a glitch or anything, and it doesn't guarantee a win in the end. The Lightning Round can be super frustrating at times, so I don't blame people for trying to find ways to make it somewhat easier.