Phase 1: Fireball Barrage
The Egg Volcanoe is a large, stationary machine that emerges from the lava. It has two main attacks in its first phase. First, it will launch a series of fireballs into the air, which then rain down onto the arena. Watch the shadows on the ground to predict where they will land and move to avoid them. Second, it will occasionally open its mouth and shoot a continuous stream of fire across the platform. When this happens, jump over the fire stream. The boss's weak point is its head/cockpit, which is exposed when it's not attacking. After dodging its attacks, jump onto the platform in front of it and perform a Homing Attack or Spin Attack on its head. Repeat this process, being mindful of the fireballs and fire stream.
Phase 2: Lava Surges and Bomb Drops
After taking enough damage, the Egg Volcanoe will introduce new attacks. The lava level in the arena will periodically surge, forcing you onto higher platforms. When the lava rises, quickly move to the safe, elevated platforms. The boss will also start dropping bombs onto the platforms. These bombs explode after a short delay, so avoid their blast radius. The weak point remains the head. Your best opportunity to attack is when the lava is low and the boss is not actively spewing fire. Use the platforms to gain height and strike its head. Characters with flight or glide can make navigating the rising lava easier. Continue to dodge and attack until the Egg Volcanoe is destroyed.