Before going to Eldin Volcano, there are a few things to be done - bring the Ruby Tablet to statue of the Goddess, and buy an Iron Shield, since the wooden one will burn very quickly. Once the way to Eldin Volcano is open, fly there just like before.
The path is straightforward at the start. Note that right after you meet the Mogma's you can jump down on a lower ledge to get 20 rupees.
Be careful in the Fire Keese cave, watch the laval level and move accordingly. The following room is a short tutorial for bomb usage. There are three destroyable walls - the leftmost one (Elevated) is 5 rupees, the middle one is your path and the right one has a giant Red Chu Chu.
As you walk past the bird statue, drop down to the small platform on your left. Take one of the bomb flowers and roll it into the opening, the crawl in to find 20 rupees.
Back on the path, take a left on the crossing to find yet another Goddess Cube. Take the right on the crossing now, past the Mogma. Roll a bomb into the Pyrup's cave.
Continue along the path. After you dispatch of the Pyrups, head forward, then right, and back around the wall to the upper most ledge. You'll find an empty Pyrup shell with 5 rupees underneath it, roll a bomb into it to get to them. Further down the path you'll find another empty shell and a Pyrup, and at the end of the path, a piece of Heart.
Go back to the area where you first fought two shelled Pyrups, take a bomb, and roll it all the way across the bone bridge leading west. If done right, it should explode next to the hole from which lava is guzzling, expanding it and draining the lava from the area above.
Go there and use the jetstreams to get up to the elevated cave. Drop down into it and use your sailcloth to get safely to the bottom (Note the Goddess Cube).
Enter the cave system to the left and talk to the Mogma. Go into the room behind him and defeat all the Bokoblins, but note that they'll keep coming until you kill the one on the top platform calling them with his horn.
Talk to the Mogma again to receive Digging Mitts.
Dig at the area where the Mogma instructed to make a jet stream appear. Up ahead, take a left at the crossing. and up the ladders. You'll have three different tunnels to slide through, pick the middle one and pick up the Eldin Ore from the chest.
Drop back down and go to the crossing again, taking a right this time. In this new room, the way ahead will be blocked by a Pyrup. To get through here, go left, right, then left at the first corner again. Go all the way up this path and you'll find a grass patch with some bombs. Now you can bomb the two Pyrups blocking your path to the exit, on the other side of the room.
There are three digging patches among the grass, the third one from the left will have a jetstream. Ride both it, and the big stream up and out of the cave.
Talk to the Mogma ahead, and using the bomb you see behind it, blow up the wall to create a shortcut to the area you've previously been in.
Approach the contracted bridge and it'll expand, allowing you to cross. Once on the other side, go past the bird statue and to to the sand slope. Sprint up to the first ledge with Bokoblin, dispatch of it and cross left to where the bomb flower is.
Drop the bomb flower down to the loose wall. There you'll find a shortcut to the very begining of the area, as well as a Goddess Cube.
Back on the ledge with the Bokoblin, use the Beetle to scare away the Bokoblin at the very top, holding the boulder, then quickly rush up. Dispatch of any enemies in the area ahead. Blow up the loose wall next to the bombs, as well as the wooden watch tower.
Inside of the cave that was blocked by the wall you'll find Tubert, who runs a game called Thrill Digger. Once you've wasted a sufficient amount of time here, go across the fallen watch tower and up the path to another sand slope.
This time around it's not possible to sprint right up the ledge with the Bokoblin, it's too high. Instead, sprint around the right side. Do the same thing for the second ledge. Now, just like before, use the Beetle to scare away the Bokoblins at the top with the boulders, and quickly sprint up.
After overhearing the Mogma conversation, you'll get the option to dowse for key pieces. The first one is in the central area near the entrance. Now go left and up on the ledge with the bombs. Drop a bomb down to the wooden tower. The second piece is underneath.
As you climb the slope back up, you'll see a small patch of water. Digging at the mound next to it will get you a jestream. Ride it up with a bomb in your hands and you can get another Goddess Cube.
On the opposite side, next to the balcony-like structure, there are two Bomb Flowers. Roll one off the edge to destroy the wall on the far end. The next key piece is in that mound.
Further right to the balcony structure is a small village of Bokoblins. Dispatch of them and use a bomb to knock down the tower. Cross the tunnel to the other side. Just as you exit, there's a small ledge to your left side. Drop down and slowly make your way across. Spring up the left wall, then sprint jump up the right one.
Sprint jump to the vines on the far wall, and make your way to the right. Don't leap, you'll run out of stamina. Pick up the stamina fruit for the last stretch upwards, and eventually you'll find yourself on the other side of the chasm.
Go through the tunnel and you'll end up in a heated area. You'll quickly die here, so run to the right and down the slide. Once you're outside quickly steer right or left to one of the jetstreams. You can now see the sand slide splitting off into two, you need to go down the right one, stopping at the ledge near the bottom. To your left you'll see two jetstreams. Ride them consecutively to reach a platform with the 4th key piece.
Ride down the remainder of the way. Jump to the platform with the 3 Bokoblin skulls and continue on that path until you see some Bomb Flowers on a grass patch. Take one and run into the cave with the big jetsream. Take a left right away and blow up the wall here. This'll create a shortcut to the previously visited areas.
Go back a bit, to where the stamina fruit was, and enter the cave here. You'll see a small lava lake and a Bomb Flower. Take it outside it throw it at the lava that's guzzling out of the wall. This will empty the room, allowing you to blow up the rock blocking your path. You'll have to roll it along the sloped right wall to have it land in front of the rock. Sprint over and get the last key fragment.
Use the big stream in the other cave to ride all the way up to the temple entrance. Pop in the key and enter.