I had this challenge in mind, I'm more familiar with the N64 Zelda's but it can work for any other one with some tweaks, including games outside of the Zelda franchise, but you'd have to alter the challenge a lil bit.
Basically:

 - Never pick up new hearts. You can pick up Heart Pieces if you need to refill your health and there's one close, as long as you don't collect four to complete a new heart (Five for Twilight Princess). This means you'll be having only 3 hearts the entire game.
 - No equipment upgrades unless necessary. So use only the first Bomb Bag only, the first Quiver...
 - (Majora's Mask) Collect all masks.
 - (Optional) (Ocarina of Time) Collect all Skulltulas.
 - (Optional) Don't use fairies to revive you.
 - Now's the real deal. If you die, reset the save file.

Other things
 - You can use hacked versions of the games to remove cutscenes, make aesthetic changes, or start the game in a place where it would be better to reset to. For example, in Majora's Mask, you can start in Human Clock Town, after the Deku section, as it's not possible to die in that part unless you're specifically searching for stuff to kill you. I'd say the same can apply to Twilight Princess' intro and starting in the Forsaken Fortress in Wind Waker.
If you can't hack the game to do that, one solution is to make a save file on the places mentioned, copy that save file to another one and play the other one. If you die you just delete the one you were playing and copy the other one again.
 - You can use remakes or remasters of the game
 - You can add any additional challenges, like, playing only in Hero Mode, but do not remove any of the challenges.
 - The previous can apply to stuff that is obtainable using hacks, like making enemies do 2x damage, or making the time faster in Majora's Mask, but don't use hacks to make it easier.
 - It's okay to give up. It happens, don't pressure yourself.
 - No deadline.
 - No reward as well, I'm not going to give you something for doing it, maybe that's for a later competition I may create.

I'm pretty sure a great amount of like, two people are going to try this out, but meh, whatever. I'll be doing it with the N64 version of Ocarina of Time (probably) and registering my progress on raffles. I prefer Majora's Mask but the game is really hard. The 3DS version of Ocarina is the superior one for this challenge (as it's more practical and fluid) but I am too lazy to learn how to mod that game. I'll be trying without having fairies revive me at first but if that doesn't turn out too good I'll maybe change so I can use fairies. Also, I will collect the Skulltulas.

I hope this turns out well.