The Fearsome Fire Beast (dragon) is the boss on the Fire planet, and you have little time to use Sir Peleas' Ice Arrow to kill it. The correct steps :
Sir Peleas is at the lair of the Fearsome Fire Beast, inside the volcano on the Fire Planet. He will give you the Ice Arrow to fight the robot dragon.
You fight the Fearsome Fire Beast (dragon) at the bottom of the volcano on the Fire Planet. You will use the Ice Arrow given you by Sir Peleas. (see the related question)
Sir Peleas is deep within the volcano, at the lair of the Fearsome Fire Beast (a robotic dragon). He will give you the Ice Arrow to defeat it. (see related question)
The "end of the volcano" is meeting Sir Peleas and fighting the Fearsome Fire beast (a robot dragon). Completing the dragon fight sends you and Sir Peleas back to your spaceship.
It is on the Fire Planet. The Fire Planet's coordinates are 83, 20.
you have to climb the ropes
You don't defeat knights, you talk to them and they'll give you a weapon to defeat a beast. (On the jungle planet, find the Laser Lance down in the plants before you meet Sir Cador.)
It is generally referred to as the TigerCopter or the Snow Panther Copter (it has the face and ears of the Pink Panther, only white).
beat the beast and let the knight join your journey
Fly to the three planets where the other knights have gone, and battle the mechanical creatures there.The Jungle Planet, at X-15 Y-15. (Home of the Phoenix Birds.)The Ice Planet, at X-73, Y-83. (Home of the Snow Panther Copter.)The Fire Planet, at X-83 Y-20. (Home of the Fearsome Fire Beast.)
The mechanical dragon (fearsome fire beast) is inside the volcano on the Fire Planet, past the lava, cinder blasts, and "eye monster". To defeat the dragon, you have to shoot it three times in its open mouth while it is temporarily turned off. Sir Peleas will give you the Ice Arrow to use. (see related question)
You get the ice arrow from him to defeat the Fire Beast (mechanical dragon). Once you have beaten all three planets, the knights will tell you of a giant asteroid. It is at X-11 Y-82. Only go there if you have all three knights with you. (see related question)