I've found the following to be the best strategy.

1. Get a Guardian potion, and a potion medal. Pouch items can't be used, but still do have an effect.
2. Save close to the dragon. This cannot be understated...
3. Practice a few rounds, figure out which boss is your hardest of the first 8.
4. When you feel confident, drink a guardian potion, when you are right next to the dragon.
5. Proceed to the hardest boss of the first 8. I recommend Ghirahim the second time.
6. Go as quickly as possible, to keep the effects of the guardian potion for as long as possible.
7. If you die, load and repeat 4-6.
8. Stop at 8 bosses.

With this strategy, I was fairly easily able to beat 8 bosses. If you are just trying to get the piece of a heart, then don't bother taking the potion.

I've found the following to be the best strategy.

1. Get a Guardian potion, and a potion medal. Pouch items can't be used, but still do have an effect.
2. Save close to the dragon. This cannot be understated...
3. Practice a few rounds, figure out which boss is your hardest of the first 8.
4. When you feel confident, drink a guardian potion, when you are right next to the dragon.
5. Proceed to the hardest boss of the first 8. I recommend Ghirahim the second time.
6. Go as quickly as possible, to keep the effects of the guardian potion for as long as possible.
7. After the guardian potion wears off, make sure to keep your hearts at full as much as possible. Know which bosses have heart supplies, and where, and try to keep your hearts full. This is more important than beating the boss quickly.
8. Be careful, try not to get hurt as much as possible.
9. If you die, load and repeat 4-6.
10. Stop at 8 bosses.

With this strategy, I was fairly easily able to beat 8 bosses. If you are just trying to get the piece of a heart, then don't bother taking the potion.