You won't be able to find extra Heart Containers in the wilderness (well, the one on the Beach is still there), but you can find bomb bag upgrades. Bombs are very important in this quest, especially when your health is low in the first few dungeons. They're a very effective way to defeat certain difficult enemies.
Dungeons have multiple entrances. If you cannot find a way forward, try leaving the dungeon and looking for another way in.
Bribery can be helpful more than once. Try each of the guy's prices if you are stuck
When you get an item that does not deplete resources, that means you should be using it constantly. This goes double for the Whistle. If you're stuck, try using the whistle.
Keep your distance from Lizalfos. As bad as their swords may be, their touch damage is much worse.
Blue Like Likes will charge at you. Try to avoid getting into positions where they line up with you.
Always kill Bombchus at a distance.
You are going to have to choose between Heart Containers and really good equipment. The game can be completed regardless of what choices you make, but I recommend being consistent (if you take equipment, ALWAYS take equipment. If you take hearts, ALWAYS take hearts).
The Lens is your friend. Do not leave it neglected in your inventory.
If you enter a dungeon and there are no doorways, it is a Gauntlet that you are supposed to return to later. These rooms have a single walk-through wall and Ama with a warning about which item will be needed to proceed. Attempting to proceed regardless of the warning will not bode well.