Help the Digging Goron
Go east from Crown Dungeon and go into the rightmost cave. Follow the path and go down the stairs at the end. Push the top rock right and the bottom rock down. Then go to the right and push the rightmost rock down and the one to your left to the left. Then you can go outside.
Go to the right and then up. Go left across the bridge. If you are playing a Linked Game, go into the cave past the bridge and talk to the Goron to get a secret. Outside of this cave, pick up the middle rock to find a time portal. Use it and go into the cave that you appear in front of. Give the requested seeds and bombs to the goron.
Plant a Gasha Seed
In the past, you can go to the left and dig in the middle of the bushes to find a spot of soft soil for planting a Gasha Seed.
Reach Rolling Ridge
After finding the soft soil described above, go back to the right, past the picture of the goron with its eyes closed, and go close to the cave near the rocks. Play the Tune of Currents to go back to the present day. Go east from the time portal and go into the cave just east of the bridge. Go down the stairs to a room where you can step on a switch to create a bridge. Cross the bridge and exit the cave on the other side. Go south and follow the path from there. Along the way you will see a small tree. If you burn the tree, don't talk to the old man down the stairs or he will take money from you.
Dance with the Gorons
When you reach cave entrances, go into the rightmost cave and then go north. You can dance with the blue goron for 10 rupees. You need to do this in order to proceed to the next part of the game.
The game consists of pressing the B and A buttons to mimic the sequence and timing that the blue goron demonstrates. When he raises his hand and opens his mouth, that means to press the A button. For all other actions, press the B button (it doesn't always look the same).When the game starts, you will hear a whistle, then the blue goron will do some dance moves. Wait for the second whistle, then repeat what the blue goron did. You have to have the correct timing and the correct sequence of moves. When you do it successfully, you will get the Brother Emblem.
Get a Gasha Seed
Go down to the previous screen and talk to the Goron guarding the stairs. Go up and use the switch hook to reach the chest that contains ten bombs. Then go left and use the stairs. Then use the stairs next to the sign to reach the entrance to the bomb game. The goron there won't play the game right now, but you can use the stairs on the right to reach the chest that you might have seen earlier, which contains a Gasha Seed.
Get the Rock Brisket
Now go outside and go west until you cross a bridge. Pick up the middle rock to reveal a time portal if you haven't already. Use the time portal to go to the past. Go into the cave up above and if you gave the goron some seeds and bombs like he asked for, you might find that he has two chests for you to open up. I'm not sure what the trigger is for this. As far as I know, they each contain a random ring.
Go outside and use the Tune of Currents to go back to the present. Go east from the time portal and go into the cave just east of the bridge. Go down the stairs and cross the bridge. Exit the cave on the other side. Go south and follow the path from there until you reach the two cave entrances. The sign here says that to the left are the Dry Falls. Go west and cut the bush to find a time portal. Use the Tune of Echoes to go to the past.
Swim across the water to the right to exit east. Swim across more water to the right and go into the cave entrance on the right. Talk to the Goron guarding the door and then go up the stairs that he was guarding. Use Pegasus Seeds to jump west until you reach stairs leading up. Go up, then use the switch hook to go over to the chest that contains 100 rupees.
Now go outside and go south to the vine sprout. Use the Switch Hook to move it over to the indented wall. Go east if you haven't already, and you will see a Mystery Seed tree. Just by seeing it, you add it as a warp point. This gives you a handy shortcut back to the entrance of Rolling Ridge in the past.
Go back and use the Tune of Currents to go to the present. Now you can climb the vines. Go east to play Target Carts. Play until you get a perfect score. You will get the Rock Brisket. The key is to face the direction that you want to shoot in before you press the button for the Seed Shooter.
Get the Goronade
From Target Carts, go west, then down the vines, then northwest. Go into the cave, go down the stairs on the left, then use the switch hook to reach the stairs to the east.
Give the Rock Brisket to the goron who was guarding the stairs. You will receive the Goron Vase. Go back up to the target cart game and lift the rock to the right of the entrance. Use the time portal to go back to the past. Go to the entrance of Rolling Ridge and give the vase to the goron who was guarding the stairs. He will give you the Goronade.
Get the Old Mermaid Key
Go outside and use the Tune of Currents to go to the present day. Go back into Rolling Ridge and head up to the bomb game. Give the Goronade to the bomb game goron. He will let you play a free game. The objective is to avoid getting hit with any bombs. Use pegasus seeds to make it a little easier. If you last all the way through, you get the Old Mermaid Key.
Get the Lava Juice
Now, leave the bomb game and go down the stairs on the left. Go outside and climb up the vines around the corner. Go to the target game, but lift the rocks to find the time portal (if you haven't already) and go to the past. Go into the Goron Gallery game up above. Play until you win the Lava Juice.
Get the Letter of Introduction
From the Goron Gallery Game in the past, go west, then hop down the ledge and go west and up and into the cave. Talk to the goron here and give him the Lava Juice to receive the Letter of Introduction. You also have to have the Old Mermaid Key for this to work.
Get the Mermaid Key
Go downstairs and give the Letter of Introduction to the Graceful Goron. You have to win the dancing game against him. You will receive the Mermaid Key.
Go to Mermaid's Cave
Now you can leave Rolling Ridge and go west. Swim into the waterfall to reach Mermaid's Cave.