Head over to the cave entrance and go inside. Note that there are little mechanical dragons outside the entrance, which can actually damage you. Use Galleth's Catapult move to launch yourself through the wooden obstacles, then drop down onto the next area when you have to. The next launch thing is high up, so you need to run on the roller to lower it, then grab on when it's at its lowest.
For this next part, launch yourself to the lower of the two moving launchers, then drop down to the stationary one, which can be used to jump to the higher moving one. Drop down onto the moving platform to get to the ground. Jump to the spire, then the next platform and use the launcher to get to the top, avoiding the fire hazards.
This is the last leg of the ascent, so use the two launchers to get to a moving one, then drop down. Run on the roller to lower the next launcher, but wait to go grab it until the two fireballs are moving away from it. Jump when it reaches the top to find a giant mechanical dragon sleeping! There's a hook on the right pillar, which can be used to launch yourself to the spire on top of it. Jump onto the horn, then the inside of the mouth when its open, then the last horn and use the rope to slide down to a cutscene.
MINI-BOSS: MECHANICAL DRAGON
The mechanical dragon is awake and you have to fight it using Carmelita. It will open with shooting fireballs that explode when they hit the ground; just run around to avoid them. Next, the middle head will lay down on the ground and fire a stream of fire from its mouth. This is your chance to attack, so aim and shoot the part in its mouth to daze it, then run to the X on the ground to get a chance to shoot the eye.
Shooting the eye will disable that head for now. The right head will shooting as homing missile, so shoot it before it hits you, then some lasers will sweep along the ground from front to back. Some tiny dragons, like outside the entrance to the cave, will appear, but avoid the fireballs first and shoot them if you want. The left head should be doing the flamethrower attack, so attack the part inside its mouth to disable it, then run up and shoot the eye.
The remaining head will now fire three homing missiles, then the dragon will try to blow you off the platform by flapping its wings. After that is some more fireballs, then the flamethrower. Once you destroy the eye of the third head, all three heads will reappear. Things are about to get a little more hectic now.
The attacks from before will start to be combined with each other, and the heads will also attack you at the same time. After the two heads shoot fireballs, the left and middle will do the flamethrower attack. It's easier to attack the middle head, so take that one out first. Do the same with the other two heads to finish the battle and the mission.
