#1 - Ze Kasho Shrine
From Akkala Tower, glide down to the northwest to spot the shrine a short distance away from South Akkala Stable.
Interact with the terminal inside and use the gyroscope to tilt the platform to make a path across.
Hit the crystal in the next room to make the blocks rotate, and use them to shield you from the lasers as you make your way across. You may need to shoot the crystal or activate it with a bomb if you get caught short.
To get the chest at the end of this room, you have to get on top of the block that rotates around the platform here. Activate the crystal from this side of the room when the block at its lowest and drop on to the top as it rises. Stay on the top until it reaches its highest position and glide down to the platform where the chest is sitting.
Proceed to the last room and interact with the terminal for another gyroscope puzzle. The objective is to get all three orbs into their slots. This is easily done by tilting the platform to the right, and then down towards you.
When you're successful, you can go through to the altar.
#2 - Dah Hesho Shrine
This shrine is to the southeast of the Tower, on top of a cliff on the east side of Lake Akkala.
There's a Guardian Scout II inside with 375 HP and one standard melee weapon.
#3 - Tutsuwa Nima Shrine
Before you head to this shrine at the Spring of Power, it's worth grabbing a scale from Dinraal the fire dragon first.
From Gut Check Rock (on the large island north of Death Mountain where Gorae Torr shrine is located) glide westward and you'll soon spot the Eldin Great Skeleton. You need to get to the skeleton by 9AM which is when Dinraal spawns next to it.
If you're struggling to find the skeleton, it's west of East Deplian Badlands in the Eldin Mountains, on the large plateau west of Eldin's Flank.
The Spring of Power is east of Death Mountain, to the west of Akkala Stable. Drop the scale into the water to reveal the shrine and complete The Spring of Power shrine quest.
There's a Guardian Scout IV inside with 3000 HP and three '++' melee weapons.
#4 - Katosa Aug Shine
This shrine is out in the open, east of East Akkala Stable.
Interact with the terminal on the right for a gyroscope puzzle. You need to get the orb onto its pedestal with a straight shot that's not too hard, and not too gentle. When you're successful, you'll activate a moving platform over to the altar.
Ignore the altar for a moment and head behind it to find another gyroscope puzzle. This time you need to aim at an angle so that the orb will roll around the chasm.
Succeeding will grant you access to the shrine's chest.
Head to the altar when you're done.
#5 - Ritaag Zumo Shrine
Make your way to the start of the spiral that leads Rist Peninsula (south of the centre).
Here you'll find an orb next to stone tablet. Read the inscription to being the Into the Vortex Shrine quest. Your job is to get the orb to Rist Peninsula at the centre of the spiral.
Achieve this by whichever method you prefer. You can walk to the middle defeating or avoiding enemies as you go, or use the powers at your disposable - like Cryonis - to get the orb to the pedestal in the middle.
As soon as the shrine appears, you can walk in and clear it.
#6 - Ke'Nai Shakah Shrine
Head to the tallest part of the mountain on the north side of Ulria Grotto.
Look south, over the water, and you'll see two updrafts. Glide to the one on the left, get a boost, then glide to the second one.
Glide back towards the cliff face on the north side and you'll some destructible rocks. Use a bomb arrow to destroy them, revealing the shrine.
Inside awaits a Guardian Scout III with 1500 HP and two '+' melee weapons.
#7 - Zuna Kai Shrine
You can pick up The Skull's Eye shrine quest from Jerra at Akkala Ancient Tech Lab after you've proven your identity to Robbie during the Robbie's Research side quest.
You can easily spot this shrine from Gut Check Rock, on the island north of Death Mountain, where the Gorae Torr Shrine is located.
Head straight to the altar once you get inside.
#8 - Tu Ka'Loh Shrine
The shrine is on Lomei Labyrinth Island which you can reach by gliding over from the cliffs near Akkala Ancient Tech Lab.
Once you set foot on the island, the Trial of the Labyrinth shrine quest will being. Once again, climb to the top to avoid Guardians - being wary of the the flying ones - and head to the position on the map above.
Glide straight down from here and climb up the ladder on the right, lit up by torches.
Follow the path and it'll lead you to the shrine, where you can head straight to the altar.