On Iki Island, there are two more Mythical Tales for you to claim some more legendary rewards. The second tale you can access is The Legacy of Kazumasa Sakai. This can be done after defeating the Eagle or maybe before. You must first locate a storyteller camped near Zasho Bay at Sheltered Campsite, which is to the east of Iki Island.
Upon arrival, you must sit at the campfire and listen to Jiro, the storyteller, talk about Kazumasa Sakai, Jin's father. A confirmation occurs, and you get kicked out of the campsite. You must sneak into the camp and listen for more information about your father's house armour whereabouts.
To do this, go to the left side of the boat, and use your grappling hook to climb up. Be careful of being seen—if you are, you'll have to restart from just after you were kicked out. Climb down the ladder, then jump onto the roof, quickly, as there is a guard who can see you. Fall down at the back of the house, then open the small hatch and go inside. Wait before the person inside goes moves, then climb down the ladder. Wait again on the ladder until the person downstairs moves, then move to where it says eavesdrop, and hold down R2, and the rest of the story will occur.
You can either sneak out or get caught. Either way, you can progress with the mythic tale. From where you get kicked out, go left through the tunnel, then go right, and there is a shipwreck you can grapple up. This is the start of a platforming section.
Head to the front right of the shipwreck and walk along the rope, and continue down the beams and ropes. Jump on the boulder, and keep going until you're on top of a second boulder, and you need to swing using your grappling hook.
Before you do this, go into the rockpool behind you and pull down a mast. If you don't do this, it's impossible to swing over to the other side. Once it's pulled down, head back to the top of the boulder, swing across using this new mast, and then grapple onto a tree stump and climb up. If you fail, you have to back to the start. The quickest way is to fast travel back to the Sheltered Camp.
Follow the boulder until you see a broken box with some leather inside. Jump on the nearby mast, then tumble into the water below because it'll break. Ahead of you is a small gap to swim under, and to your left is some land you can climb up.
Head towards the shipwreck to your left on the land, and you can grapple a piece of timber. This will rotate the shipwreck, making it accessible to climb upon. Do just that and follow the wreckage and jump on the boulder. Once again, swing on a grapple point and aim for the pool beyond the rocks.
When in the pool, look to your left, and you'll see a rowing boat with a mast you can grapple. Do just that, then follow the pool behind you, through the small gap you can step through, then take another right underneath a gap in a shipwreck you can swim under.
Then head back to the grapple swing you used to get into the pool, but this time grapple onto the mast you just pulled free. There's three swings to be had, and you'll land on top of a boat.
On this shipwreck, grapple the mast, and it'll fall over. Hop on it, and walk along it, and follow the rope. Now, this part is annoying, as you have to time the jump correctly, or the waves will knock you off, and you have to start from the beginning.
After a wave has splashed on the seaweed-covered rock in front of you, jump on it, then immediately grapple onto the mast to swing to the next seaweed-covered rock. On the second rock, jump/grapple onto the rope above and make your way to another mast. From there, you've got two more seaweed-covered rocks to jump onto to reach the bounder/shipwreck beyond. Time these right, and always jump after as wave has smashed into the rocks.
When past the rocks, jump into the water, keep to the left, and you'll see a slope leading up to some rope. Cross the rope, jump onto another seaweed-covered rock after the wave, then grapple onto the grapple point on the boat and climb up and get into the boat itself. And then before you is the Kazumasa Sakai Horse Armour.
When the horse armour is equipped, your new ability Horse Charge will inflict more damage, and all attacks are less likely to dismount Jin.
For more guides on Ghost of Tsushima Iki Island, we have you covered.