Before going on to the third Beast, it is very useful to visit the region east of Death Mountain. Travel to the Sah Dahaj Shrine (north of Foothill Stable), then go northeast and you'll soon find another stable.
South Akkala Stable
Talk to Rex who tells you about the legendary sword, which chould be near Death Mountain or near the Woodland Stable. Talk to Kaifa, who tells you about a strange man Kilton whom you can find near Skull Lake to the north and who manages a shop "Fang and Bone". Then go west to find another shrine.
Ze Kasho Shrine - Ze Kasho Apparatus
Go ahead and look at the terminal. Move the scale to create a spike-free path, then jump and go forward. Hit the switch, then quickly go until half the course while the blocks are rotating. Shoot an arrow at the switch, then run until the end of the course. To reach the chest on the right, shoot another arrow, then climb onto the block which moves up from the left and stay on it. Then hover to the chest and find a Silverscale Spear. Keep going and look at another terminal. This time, you have to place each ball on each switch. Then, go right and climb the steps. Look at the Sheikah symbol and the monk Ze Kasho gives you another Spirit Orb.
Now head south to find a path, then go round or climb the hill southeast and you reach the Akkala Bridge Ruins. Hit the Moblin that is attacking a man, then talk to Nell. He tells you about Akkala Citadel, which was used by the Hyrule army when the castle was attacked. Then he warns you about the Guardians which stand guard around the fortress. Go northeast, get rid of the Bokoblin and pick up its Spiked Moblin Spear if you want to.
Beware of the scouts and climb the steps to the left. Get rid of another Bokoblin, then of an archer Bokolbin, and look at the scout. Climb on the rocks to the right to avoid it, then climb the citadel's walls. Go until you reach the crates, then when the scout has gone by, reach the stairs again and run. Climb again to avoid the next scout, then dash at the Moblin and the Bokoblin and fight them. Climb some other rocks to avoid the last scout, then notice the pink substance around the tower.
Attack another Bokoblin next to a campfire, then cook if you need to get some strenght back. Climb the little ruin and find some Bomb Arrows in the chest. Shoot some Fire Arrows (by using the fire) at the archer Bokoblin on the other side (west), then hover to it. Throw a bomb at the blue Bokoblin, go ahead, get rid of another Bokoblin (and pick up its Dragonbone Boko Bat), then look for a hanging eye at the ceiling. Shoot an arrow at it, and some pink substance vanishes. Open the chest for 100 rupees. Climb on the small wall and jump towards the tower. Climb up for roughly 2 meters (or 7 feet), turn right and look for a place to stop, then turn round and fly towards the bottom of some stairs. Fight the Bokoblin, then climb the ruin by turning towards the right to avoid the substance. You then just have to fly towards the tower and to climb it to the top. Place the Sheikah Slate on the terminal to get the region's map.
Now fly north, then follow a path heading northeast. You can also travel back to the stable and take a horse. If you meet them, talk to the riding traveler, who knows a woman named Nobo who knows a lot about the Spring of Power, and to Pitar, another riding traveler, who tells you about Fang and Bone at Skull Lake. If you come across some scouts, go round them by the east. You finally reach...
East Akkala Stable
You meet there the painter Pikango who can tell you about another picture. Talk to the guard Hoz who also knows Kilton (who wanders around with a cart at night) and asks you for a detailed sketch. Talk to Aya who regrets her blue flame, and says that the Ancient Tech Lab's director didn't come for a long time. Talk to Nobo as well, who knows the fountain and the Spring of Power located to the west. Take the Woodcutter's Axe if you don't own an axe. Close by, some signs point to the Akkala Ancient Tech Lab towards the northeast, and a few meters away stands another shrine.
Katosa Aug - Katosa Aug Apparatus
Go right and look at the terminal. Move the lever to the right to push the ball into the container to the left, which activates a moving platform. Cross on this platform. If you want what the chest contains, go behind the monk's pedestal and look at another terminal. Same thing here, but this time, the ball has to go across the hole (with a sharp move) or by bouncing off against the top fence to reach the left container. Use the platform to get a Great Frostblade from the chest, then go back to the monk, look at the Sheikah symbol and the monk Katosa Aug gives you another Spirit Orb.
Now aim for the west, and down the plain, you'll spot a small lake. Go into that lake, it's the Spring of Power. Touch the pink cloud to get a memory... You remember princess Zelda in this fountain talking about the power of the seal passed down from mother to daughter, but unfortunately Zelda doesn't feel anything regarding this power. Pray in front of the goddess statue, and it asks you to offer a scale of Dinraal, the red spirit, to the Spring of Power. Next, go back to East Akkala Stable, then go on to the north. Beware of the two active Guardians, go a big roundabout way to avoid them, and you reach the...
Akkala Ancient Tech Lab
Get in and talk to the kind of... device. Then Robbie and his assistant arrive. Talk to him but he wants to see your scar. Take off your shirt to show it to him. He's the Guardian researcher and director of this lab, and he wants you to help fight the Calamity. For this, he can supply you with Ancient gear, but he as well needs to light his furnace again with a blue flame. Talk to him again to learn you have to go to Tumlea Heights west from here. Then talk to Jerrin, Robbie' wife and shrine specialist. She tells you to go see the left eye of Skull Lake (the one higher up) to find a shrine. Pick up the torch near the desk and read Robbie's memoirs to learn what happened a hundred years ago.
Leave the lighthouse and go northwest to go round a lake, then keep going southwest where Tumlea Heights are. Look for the blue flame furnace sheltered inside a rock in the centre of this area, then light the torch in the furnace. Obsiously, if it's raining, you'll have to wait a little... As for Hateno Ancient Tech Lab's furnace, you have to light the torches along the way to bring Robbie the blue flame back.
There are two strategies: looking for lanterns while avoiding the enemies OR after earch lantern lit, putting away the torch, fighting the enemies, looking for the next lantern then coming back to the previous lantern. From the furnace, you have to light up a lantern to the east, then head south, go round the lake, then go back north, and when you are blocked by rocks, walk cautiously east (because of the Guardian) and go on north up to the furnace which stands in front of the house. If the Guardian is difficult to sneak past, then destroy it by raising your most powerful shield and sending back its shot by pressing A at the right time. When you light the lab's furnace, a travel point is created. Enter the old lighthouse and talk to Robbie. To thank you, he gives you three Ancient Arrows. He tells you that his "cherry" can create other Ancient weapons and for this, you have to give it Ancient materials and rupees. Talk to Cherry to see the available weapons and their prices.
Check your map and aim for Skull Lake, northwest of the region. From 8 pm on, on the lake where the "left eye" is, you can see a weird coloured cart. Get close, take a picture of the "creature" and talk to Kilton. He's a merchant buying monster materials for a really good price. Tell him that you like monsters just like him, that's why he opened Fang and Bone. Then he disappears to settle somewhere else... to Lake Akkala.