Entrance to the Second Quest
At the name entry screen enter: Zelda.
Fewer enemies
Kill all the enemies except for one in a particular screen, and next time you go through there will only be that one enemy there, instead of them all coming back.
Magically Unlock A Door
As soon as you enter Level 1, exit. Then, go back into Level 1. You will notice that the northern door is now unlocked.
Refill Red Water of Life
If you bought a red-colored Water of Life, when you use it once, it turns blue, meaning you can only use it once more before it disappears. To refill it from blue to red without buying a second Red Water of Life from the Old Woman, buy a Blue Water of Life. Doing so will make it red again.