This page explains how to find the Shae Katha shrine.
How to Reach the Shrine
You might want to activate Lake Tower before you look for this shrine.
To open the shrine, you will need to obtain a Farosh's Scale.
One way to reach this shrine is to go southwest from Shee Vaneer Shrine. Another way is to float northwest from Faron Tower. Yet another way is to go east on the road near Pumaag Nitae Shrine, then go north after you cross the river.
The shrine is north of Dracozu Lake, inside of a stone structure that is shaped like a dragon's head.
Talk to the Goddess Statue inside of the dragon's head statue to receive the shrine quest.
Then hold a Farosh's Scale and drop it into the spring in front of the Goddess Statue to reveal the shrine.
About the Shrine
The chest in the shrine contains a Thunderspear.