Phase 1: Dividing the Smog
Smog is a boss composed of several smaller smog clouds that float around the room. Your goal in this phase is to divide the large smog cloud into smaller, manageable pieces. Equip your Cane of Somaria. Use the Cane of Somaria to create a block. Then, push the block into the large smog cloud. This will split the large cloud into two smaller ones.

Repeat this process, using the Cane of Somaria to create blocks and push them into the smog clouds, until you have divided the smog into eight tiny clouds. Be careful to avoid contact with the smog clouds, as they will damage Link. The room also has conveyor belts, which can make positioning tricky.
Phase 2: Eliminating the Small Clouds
Once you have eight small smog clouds, they will begin to merge back into larger clouds if left alone. Your new objective is to eliminate them before they can reform. Equip your sword. When a small smog cloud is isolated, quickly attack it with your sword to destroy it. You need to be fast and precise.
Focus on destroying one small cloud at a time. If they start to merge, you may need to use the Cane of Somaria again to split them. Continue destroying the small clouds until all eight are gone. Smog will be defeated, and you will receive a Heart Container and the Burning Flame (Essence of Time).