After you emerge from the Pit Cave and explore Great Sky Island further, you discover Bottomless Cave.
Explore the Cave
Near the entrance of the cave, you find a Bubbulfrog, but be careful when swinging your weapon, because there are bomb flowers in the ground that will explode if you hit them, and since you only have three hearts, you probably won't survive. You can pick up the Bomb Flowers to take them with you.
There are two slopes going north, a left and a right. Go up the left slope first to find a chest that contains Amber.
Defeat the Like Like
Go back and this time go up the slope on the right. At the top, you will find a Like Like. If you approach it, it will extend its mouth toward you and try to eat you. You can shoot the glowing stone that it sticks out of its mouth, and this will stun it, allowing you to hit the glowing stone with a weapon. Or you can get the Like Like to eat a bomb by dropping (not throwing) the bomb near it. To do so, hold a Bomb Flower and press the indicated button to make the Bomb Flower go far away, then when the Like Like extends its mouth toward you, drop the Bomb Flower in front of it. The Like Like will eat the bomb, then will be stunned momentarily The Like Like will drop a chest when defeated. It also drops a Like Like Stone.
Continue going up the path and you will find a Like Like on the ceiling. Defeat it as before, then open the chests, then go out through the west exit of the cave. Remember to eat some Cold Resistance food if needed.
Reach the Shrine
The shrine is above you, so go counterclockwise up the slope to find a hill with a fallen log and some trees. There are sharp stones on the ground that you can fuse with tree branches to turn them into stone axes and cut the other trees down. Do this, then look for the dent in the icy cliff wall. Attach two or three logs end-to-end, then place the log upright against the dent in the wall. You can then jump onto the log and climb up to reach the higher cliff.
At the top, you find another stone structure. There is a cookpot, and you will see some flint on the ground next to it. (If you lose the flint, just drop another on the ground next to the cookpot.) Hit the flint with a metal weapon to start the fire under the cookpot, and then you can use it to cook.
Go west from there to reach the shrine. Check on the glowing object to open the shrine, and go into the Gutanbac Shrine.