Good luck. But remember that the Deku Shield and Mirror Shield are required items in the game.
Also, I'm doing a three heart run
like the one you're going to do (I'm using the required items where they help and only got the bottle with Ruto's message, Megaton Hammer doesn't work well on Dark Link, just saying). I can't give much advice except work on your dodging skills along the way. Also, having one bottle doesn't make that much of a difference if you use the Blue Fire wisely.
Also, if you do end up changing your mind and using the required items where they help, use Deku Nuts on Stalfos (throw a Deku Nut while they're attacking will stun them, then use the jump attack, it helps a ton) and use Din's Fire on Dark Link. Din's Fire will kill Dark Link in three hits (affordable with max magic) on a 3HR.
Again, good luck dude.
I'm currently doing a 3 heart challenge ... No wallet/weapon upgrades, no magic/defense upgrades, no skultullas, no sun's song or epona's song, no biggoron sword, no extra bottles (only the 1 you get with the letter in it). No Nayru love or Farore wind, no Ice arrows (which I almost never get anyway).
I stand corrected, this is closer to the 3HR I'm doing. But, I'm not getting the Fire Arrows or doing any shopping (outside the Deku Shield).
By no shields do you mean not getting the Hylian shield? That's a little too extreme IMO. For one thing you may not be able to survive the trip up Death Mountain as a kid with only 3 hearts. Now if you mean only using a shield when you have to use it in order to proceed (for example light reflections in the Spirit Temple), that would be a heck of a challenge, and it would take an awful lot of discipline to not use it to block when I instinctively do so during Stalfos fights or whatnot.
Actually, it's entirely possible to get up Death Mountain without the Hylian Shield. Just keep rolling and you should make it (I should know because I did it
). And yeah, curbing the habit of defending would be tough I'll bet.