Gralens at Monster-Control HQ asks you to investigate reports of an unknown three-headed monster.
Quest Location
If you have completed WANTED: Molduga, WANTED: Hinox, and WANTED: Stone Talus, you can start this quest by talking to Gralens in the Emergency Shelter in Lookout Landing, and ask him about the unknown three-headed monster.
How to Complete the Quest
Before you go, you might want to gather as many eyeballs and wings as you can (i.e. Keese eyeballs and wings, Aerocuda eyeballs and wings). They will be very helpful in the battle. You can look for large groups of Keese near caves, and shoot a bomb arrow into them to take down a large number at once.
Also, make sure that you have a lot of arrows. You can purchase them from the shop in Lookout Landing, as well as in Hateno Village, and from Beedle at every stable.
You might also want to eat heat-resistant food or drink heat-resistant elixir, or go to Kara Kara Bazaar in southwest Hyrule to buy the Desert Voe Headband, which provides heat resistance.
When you are ready, you can either launch yourself from the Popla Foothills Skyview Tower and float southwest to the middle of the Bridge of Hylia, or go south from Kamizun Shrine to find the Bridge of Hylia. If you are riding a horse, you should leave your horse at the north end of the bridge. It will be too dangerous to ride a horse on the bridge.
In the middle of the bridge, you find a Flame Gleeok. Whenever it shoots beams of fire at you, run far away to get out of range. To defeat it, you first need to shoot the eyeball of each head until all three heads are stunned. If you have Keese Eyeballs and other eyeballs in your inventory, attach them to arrows to add a homing effect, making it much easier to stun the heads. When all three heads are stunned, the Gleeok will fall to the ground, allowing you to run up to it and hit its heads. As soon as it gets back up, run away, because it will blow gusts of wind at you, knocking you down. When you are at a safe distance, start shooting again.
If it flies partway up in the air, it will spit small fireballs at you. Move away from where the fireball is going, to avoid getting hit.
If it is flying higher up in the air, jump off of the bridge and attach wings to arrows to make them go farther, and shoot at the Gleeok's eyes while falling, because if the Gleeok gets too far away, it will shoot a huge fireball that is difficult to survive. If you aren't fast enough to prevent the giant fireball, glide under the bridge, then wait for the giant fireball to go away, then use Ascend to get back on the bridge.
After you defeat it, talk to Gralens and tell him that you hunted the three-headed monster.
Quest Reward
Gralens gives you 100 rupees. If you have also completed Unknown Sky Giant and Unknown Huge Silhouette, Gralens gives you a Diamond.