Gralens in the Emergency Shelter requests your help in defeating a Molduga in the East Barrens of Gerudo Desert.
Quest Location
To start this quest, talk to Gralens in the Emergency Shelter in Lookout Landing after you have completed two of the "Bring Peace to...!" quests. Then talk to him again and ask about large monsters, and ask about the Molduga.
How to Complete the Quest
Go to the quest destination on the map, and you will see a trail of moving sand where the Molduga is swimming. Don't walk on the sand near it, because if you do, the Molduga will hear you and it jump up out of the sand beneath you and swallow you. To prevent that from happening, stand on a solid rock. The Molduga can't swallow you there, and you can shoot arrows at the sand near the Molduga to make it come over and jump out of the sand. This allows you to attach a bomb flower to an arrow and shoot the Molduga while it is in the air. It will be stunned, and you can run up to it and hit it repeatedly. As soon as it starts to get up, run back to stand on a rock. Repeat the process until it is defeated.
Talk to Gralens in the Emergency Shelter in Lookout Landing and tell him "I hunted something" to complete the quest.
Quest Reward
Gralens gives you 100 rupees. If you have also completed WANTED: Hinox and WANTED: Stone Talus, Gralens also gives you 300 rupees.