Intermission (1-2)

 Now we have some time to kill before entering Dungeon 2. There's something very important we have to do between :20 and :28 on the clock.
This wouldn't be a bad time to go to screen H-6 and get the Letter from the old man (it's very accessible compared to the original Zelda). Now, if you ever wander across a Medicine Shop, you can buy stuff.
If you still have time to kill, the Fast Forward button is your friend (its default on ZSNES is the ~ key). Just clear a screen of enemies and hold it down and watch the minutes tick by.
When the clock is between :20 and :28, head to screen H-7. You should notice a Heart Container. Proudly pick it up. If the clock's past :28 and you didn't get this, I'd suggest fast forwarding it until the clock reaches :20 of the next hour. You can't get this Heart Container ever again after you beat Dungeon 2, so it's in your best interest to get it now.
After that's taken care of, you can make your way to Dungeon 2. Go to the beach that starts on screen H-6, and follow the path until you get to this rock (G-4). Bomb this spot to reveal Dungeon 2's location. If you don't have any Bombs, you can kill Blue Octoroks until they drop some, or you can buy some at the shop on screen E-7.