So far I've played through regular mode and Hero mode of the game, but without limitations. Now I've just started my third run (on regular mode) as a minimalist run. This means no heart containers, no shields, no potions, only one bottle because you need it and no upgrades. I'm at the start of Lanayru Desert now (3:12 hours and I had to sit through all the cutscenes :/) and didn't have a game over until now. The only time I got close was in the Ghirahim battle because I play on Dolphin and disabled the speed limit to make cutscenes faster. But this also made the Ghirahim battle faster (~50fps instead of 30) and therefore I got hit a couple times by his charge attack because I tried to counter and didn't get the timing right. After failing 2-3 times I just backflipped after that and had no problems.
The second boss was surprisingly easy, no damage. Same for the Lizalfos, I only got hit once by the first one. And I never finished the miniboss (2 Lizalfos) that quickly, never knew that you can spin-attack and subsequently fatal-blow them once you hit them one time when they're in the "mocking position". Didn't take longer than 30 seconds...
After all going shieldless is much easier than I'd have expected, only the octorocks gave me problems, it took a while to get down the timing for slashing back their bullets with the sword.
But things are going to be very hard when doing the same run in Hero Mode, and I'm not even talking about doing a boss rush.