Go back to Kakariko Village and go see Impa. She notices the Master Sword and understands that you calmed down the four Divine Beasts as she can feel the presence of the Champions. She says that you must now go to Hyrule Castle where Calamity Ganon is lurking. Warp to the Bosh Kala Shrine next to the Proxim Bridge (east of the Great Plateau) and cross the bridge. Then cross the river and go north. Cross the Owlan Bridge to the west, then keep going north. On top of a hill, there is a tree stump. You can climb on it then shoot some arrows at the three moving targets to make a Korok appear. Keep going north a little and you find a new stable.
There is a Wooden Mop and a Woodcutter's Axe outside. Talk to Gotter who asks you to go fetch a cookbook at Hyrule Castle, as well as to Parcy in the tent looking for some royal guard's weapons. You may also meet a traveling horseman, who gives you advice for fishing. And you meet again the painter Pikango and the merchant Beedle. More to the north a shrine can be found.
Wagoh Katta Shrine - Metal Connections
Climb on the cages on the right and open the chest containing some Amber. Notice the plate on the right and the monk in front, then jump down and move the crates next to the plate. Climb to the top and use Magnesis to place the plate down. Then move the crates next to the monk (not awfully close to), then place the plate between the crates and the monk's platform. Finally climb on the crates, and walk on the plate to go to the monk. Look at the Sheikah symbol and receive another Spirit Orb.
Keep going northeast, avoid the traveler next to a tree (it's a Yiga) and cross the Horwell Bridge towards east. Avoid the injured woman as well, then go east, cross the Eagus Bridge and keep following the path going north to reach the...
Talk to Kass, the Rito musician, who sings to you an old song about what happened a hundred years ago (that you may have already heard). Talk to little Ami who tells you about a secret route, the East Passage, leading to Hyrule Castle. Quince tells you a long story about the dog Satty that saved his life and a shiny beast on a strange mountain, Satori Mountain. You meet again the painter Pikango and Beedle, who gives you an Ancient Arrow, useful against the Guardians. There is a Woodcutter's Axe if you're interested. A little more to the west is another shrine.
Kaya Wan Shrine - Shields from Water
Use Cryonis to create an ice pillar next to the edge on the other side, then climb it. Then create an ice block on the running water to climb and reach the following room. Shoot an arrow at the Guardian to make it fall into the water, then create an ice pillar under the chest. Climb it and pick up an Ancient Core from the chest. Create another pillar further, then pick up the Ancient Screws that fell into the water, climb the pillar and jump. Shoot an arrow at the Guardian to get rid of it, then jump on a raft, get rid of the second Guardian, then when the raft is falling down, fly to the monk.
Since a long way is awaiting you, you can go back to the stable to bring a horse along. Go north following the road, then after going by Crenel Peak, keep going northeast and cross the Thims Bridge. Read the signs on the other side and keep going north towards Hyrule Ridge. Once you're at the Woodland Stable, keep going west until you see a headland to the south on your map. Get off your horse, then get close to the castle. Go down until you reach the sand, a bit west of the headland, then notice a pier on the other side of the river. Put on your Zora outfit and swim to this pier.
To tackle the castle, I recommand having at least 15 hearts, 5 stamina gauges, a few Ancient Arrows, the Hylian outfit boosted to the max, the Zora outfit, maybe a few pieces of the Barbarian and Ancient outfits, some meals to refill all your hearts, and meals to boost your attack.