Gralens at Monster-Control HQ asks you to investigate reports of an unknown sky giant.
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 sky giant.
How to Complete the Quest
To reach the quest destination, use the Rospro Pass Skyview Tower and go northwest to the quest destination. You will see a floating platform with a balloon attached to it. Land on this platform and hit the balloon, then when you have gone far enough, glide to the shrine on the nearby island. This is Ijo-o Shrine.
From there, you can use the Zonai device dispenser if you wish, then glide down to the island beneath this one to find the Flux Construct.
You can use Ultrahand to pull blocks away from the Flux Construct's body, but be prepared to run away if the Flux Construct is about to attack. The glowing cube is vulnerable to attack. You can either try to pull the glowing cube away, or just keep removing non-glowing cubes, because the Construct will eventually collapse if you remove enough cubes. Then run up to the glowing cube and hit it repeatedly. The Construct will swap the positions of the glowing cube, making it difficult to grab it.
Later in the battle, if the Flux Construct floats up in the air, dodge the five cubes that it throws at you, and then you can use Ascend to get on top of it, and from there you can hit the glowing cube.
After you defeat it, it drops a Flux Construct I Core that you can fuse to a weapon. It also drops a treasure chest that contains an Old Map, which marks the location of a treasure in the Depths.
Then talk to Gralens and tell him that you hunted the sky giant.
Quest Reward
Gralens gives you 100 rupees. If you have also completed Unknown Huge Silhouette and Unknown Three-Headed Monster, Gralens gives you a Diamond.