To complete the Song of the Hero, you need to go to Lanayru Desert and learn the Thunder Dragon's Song.
Golo Game-Breaking Glitch
The Thunder Dragon
The Thunder Dragon is in Lanayru Desert. The dragon is south of Lanayru Caves, so descend to the Ancient Harbor Bird Statue. Use the Clawshots on the columns on the east side to return to Lanayru Cave.
When you do talk to Golo, he will say that he found a passage where he had been digging. If you paid him, you will get paid back ten times what you invested.
Roll a bomb into the rocks in the small passage to get rid of the barrier, then crawl through. You will reach a small cave. You can strum the harp near the butterflies to reveal a Gossip Stone.
Lanayru Caves
Go outside, save at the Bird Statue if you wish, and turn west. Use the Beetle to pick up the bomb from on top of one of the cacti, and drop it on the bombs onto the rocks to the west. Then you can jump across and read the sign by the door, which says that you can only enter with permission from the Thunder Dragon.
Go down the slope that goes south from the locked door. At the end of the slope, look southeast to see a sparkle on a distant column. Use the Beetle to retrieve the key. (You can't skydive down to it because if you did, there would be no way to get back up again.)
Go north to the locked door and go through.
Bringing the Crystal to the Dragon
Go to the end of the path, where there are some Peahats. Use the Clawshots on the Peahats to reach the other side. In the area with the robots, go to the side of the mine cart and thrust with the sword to activate the crystal in the mine cart. Then talk to the robot, and the mine cart will automatically start moving. Step on the switch and go through the door before the mine cart goes too far away. You don't need to hurry too much; just make sure to stay near the cart. Kill any Technoblins and Babas that get in your way (it is recommended to use arrows to kill the Technoblins quickly). At the end, step on the switch to allow the cart to proceed.
In the next area, go over the bridge as it appears, and kill the Technoblins that appear (but wait for the sinksand to turn into grass before you step on it). Once you are near the door, there is no need to hurry. Use the Clawshots to reach the vines to the right of the door, then step on the switch to open the door to the next area. Hurry through before the cart goes too far away.
Jump onto the bridge and climb up the vines when they appear. Go to the platform with the Deku Baba. The mine cart will be stopped by the door, so no need to hurry. Kill the Deku Baba, then Clawshot over to the vines and step on the switch. Get your Clawshots ready, then use them on the vines that appear on the south wall. Climb to the left, picking up stamina fruit when you can. Leap past the gaps when the air isn't blowing through, but don't be too hasty. If you are too close to the left side of the timeshift when you try to jump across the vine gaps, you are more likely to get knocked off by the air. At the end, hop down onto the platform that appears. When the mine cart stops, use the Clawshots on the targets on the stalactites and then step onto the button.
Look east and use the Clawshot targets when they appear on the stalactites to make your way across. At the end, Clawshot the vines above the arch when they appear. In this passage, a bunch of green Chuchus will attack. Kill them all, then kill the Babas up ahead. The cart will stop at the bars. Use the whip to pull down the red bar on the other side.
There will be a large Green Chuchu up ahead, and then some blade traps that go side to side along the path. Go past them, then kill the Technoblin. Get out your whip and use it on the bars to swing across, but remember not to jump to the other side until it has turned into grass. Otherwise you will sink into the sinksand. Kill the Babas that appear from the ceiling, then stand next to the mine cart so that it will block the blade traps. You might need to switch to the other side of the cart before you are past all of the blade traps. When the cart stops at the door, the electric barrier will go away. Run up the sinksand ramp, collecting the stamina fruit as you go, and pull the bar. Let go of the bar quickly before the ground beneath you turns to sinksand, and go through the door.
A bunch of enemies appear in the circular room ahead, including Technoblins, Sentry Robots, and Beamos. Don't worry if you don't kill them all; many of them will disappear when the mine cart gets too far away. Kill the Beamos that blocks the path of the mine cart. Kill the two Beamos next to the door, then step back and target the red bar to pull it down with the whip. Go through.
Cross the bridges that appear. Kill the Babas that get in the way. Jump the gaps. When the cart stops, use the Beetle to catch a bomb and dump it onto the rocks in the way. Be careful of the Quadro Baba up ahead. You will then return to the dragon's area. When the mine cart stops, the crystal will turn the whole region into the past and the dragon will come back to life.
When you talk to the dragon, he explains that he is too ill to sing, but he mentions that the robots planted a seedling from the Tree of Life. Its fruit is said to cure any illness.
Go toward the withered tree that you see in the distance. When you reach the sinksand, run across it to get up onto the platform with the tree. Blow away the sand pile with the Gust Bellows, then hit the crystal to make the area go into the past. Send the Goddess Cube into the sky with a Skyward Strike while you're here, to unlock a chest in the Thunderhead that contains a Small Quiver. There may also be Ancient Flowers and Dragonflies around the Tree of Life Seedling that you can collect.
Dig up the seedling, and the nearby robot will talk to you. You will take the seedling with you and can plant it to turn it into the Tree of Life.
To go back toward the dragon's area. You can't get across, but you can use the Beetle to bump into the side of the mine cart and reactivate the mine cart's crystal.
Fly to green column and descend at the Sealed Grounds Bird Statue. If you haven't learned the Water Dragon's song yet, you can only go down to the area around the Sealed Grounds right now, and if you do not have the seedling, you will have to fight a boss as soon as you go down to Faron Woods.
If you DO have the seedling, then go into the Sealed Grounds Temple and use the Gate of Time. Plant the seedling in the area where Groose was (will be) standing when he said that you should plant a seedling. Then go back through the Gate of Time to find that the seedling has grown into a Tree of Life with a big fruit on it. Do a roll attack into the tree and collect the fruit.
Return to the sky and fly to the yellow column. Descend to the Lanayru Gorge statue and give the dragon the fruit. He will sing his part of the Song of the Hero.
Thunder Dragon's Lightning Round
Now that you have cured the Thunder Dragon's illness, you can talk to him to replay previous Silent Realms, or you can take his Battle challenge, known as Thunder Dragon's Lightning Round, which is a boss rush. You can choose from all of the bosses that you have fought previously. After each successful battle, you will get rupees or a random treasure item, and the Thunder Dragon will ask if you want to continue, but he will pick the next boss that you have to fight, and you won't regain health between fights. If you stop after four consecutive wins, you get a Piece of Heart. If you stop after eight consecutive wins, you will get the Hylian Shield, which is resistant to fire and electricity, and is indestructible.
Learn the Other Songs
If you haven't learned the other dragons' songs, you can go to the red column and visit Eldin Volcano to learn the Fire Dragon's Song, and go to the green column and visit Faron Woods to learn the Water Dragon's Song.
If you have learned all three, visit Levias in the Thunderhead to learn the Song of the Hero.