After you complete Mineru's Construct, you can use its abilities to cross the Depths and reach the secret stone.
Learn the Construct's Abilities
Talk to the Construct to hop on. You can then ride around on top of the Construct. If needed, go to the nearby Lightroot to restore any broken heart containers. Then go onto the platform north of the Lightroot.
After some dialogue, press the Attach button and approach the objects on the shelves. You can move around to choose which object to attach. When you are connected to the desired object, press the button to attach it to the desired body part. Be sure to attach something to each body part before you go. Be aware that once you attach something, there is no way to detach it; you can only replace what has been attached.
After you have attached something to each body part, try pressing the buttons for each body part to see what it does. Then you can go toward the destination.
Go to the Destination
As you go along, keep in mind that you will be using energy as you go. However, your energy will recharge if you stop moving, so do that as needed, or just use Zonai Charges.
Go to the platform east of the Construct Factory. There are Moblins guarding the platform. Defeat them. Be aware that you are not protected from damage while on the Construct, so try to avoid taking damage.
After you defeat the Moblins, go onto the platform, and there will be some dialogue. You can attach something to the Construct's back to improve mobility. The Hover Stone doesn't do anything, so either attach a fan or a rocket. Just keep in mind that the rocket disappears after a short time.
There is another glowing armory platform to the southeast. Go there and defeat the Moblins on the way. Try not to get too close to the next set of enemies as you battle. There are Lizalfos and a Bokoblin closer to the platform.
At the next platform, attach either a beam emitter or cannon to one of the construct's hands, then aim at the Fire Keese to defeat them. Then make your way south to the Lightroot, using the fan or rocket on your back to reach it quickly, so you can avoid the Horriblins to the right.
From the Lightroot, you can see a Hinox to the south. You can try to go up the nearby slope to avoid it.
At the armory south of the Hinox, be sure to attach a cannon to one of the Construct's hands. Then go southeast and shoot the boulders with the cannon to get them out of your way. Beyond the boulders, there is a large pile of Zonaite deposits that you can hit with the cannon if you wish, but if you lose your cannon, you should go back to the armory to attach another.
Look south to the next armory and you will see a large number of Bokoblins. Shoot them with the Cannon to try to defeat as many as possible before they come up to attack, but be careful not to let your energy completely deplete.
At the next armory, attach a rocket to the back part of the construct, and attach a spiked ball to a hand if you need one. Go to the cliff in front of the temple, and use the rocket that you attached to the Construct's back part, and push forward on the control stick to reach the upper ledge. You have now reached the Spirit Temple.
Examine the owl statue in the temple. After the cutscene, you will have to battle the Seized Construct.