This page explains how to start and complete the Lynel Safari side quest.
How to Begin the Quest
Before you can start this quest, you have to reach Zora's Domain, talk to King Dorephan, then talk to Muzu in the plaza and agree to look for 20 shock arrows. Then you will be able to receive the Lynel Safari quest from Laflat, who is near the eastern bridge leading out of Zora's Domain.
How to Complete the Quest
Go east from Zora's Domain to reach Mikau Lake, and wear the Zora Armor to go up the waterfalls. At the top, make your way up the mountain. If this is your first time there, you will automatically hide from the Lynel. After that, you can carefully take a picture of the Lynel, then go back to Laflat and show it to her. She will give you the Zora Greaves.