During the first phase of the battle, the boss is immobile for the most part. It initially attacks by swinging arms at you. Dodge the attack and pull out your Whip, using it to hit the valve on its unarmed arm. Repeat this with the other arm.
Once you do, the boss’s chest will be open to damage. During this time, the axes from two of the arms are thrown at you, and the other arms try to slam you like the other two before it. Run to the weak point and start slicing. After a period of time, you’ll repeat the process thus far until you deal a certain amount of damage.
The boss then enters its second phase. Koloktos becomes mobile, walking around with some giant legs and also wielding six swords (the weak point is guarded by a cage, now). During the boss’s slicing rampage, stay a fair distance back. Eventually, though, three arms will slam down. Unfasten the valves on one arm with the Whip, then pick up the dropped sword.
If possible, slice the boss’s torso in a horizontal manner, then hit the cage two/three times, opening up the weak point. You may want to drop the sword now and use your own sword to do damage (it slices faster). You’ll soon have to repeat this process until the boss is defeated.
After the battle, snatch up the Heart Container and go through the door on the other side of the room. In the next room, go forward and hit the crest with a Skyward Strike. You’ll end up purifying your Goddess Sword with Farore’s flame, transforming it into the Goddess Longsword, which can deal double the previous amount of damage.
Fi will then tell you that you ought to return to the Isle of Songs, then you’ll be teleported outside.