Dragon Slayer
Start: Talk to the Guild Master of the Champion's Guild about the Rune Platemail.
Skills: Able to defeat a level 83 Dragon, and level 37 or 43 prayer is helpful.
Quests: Must be a member of the Champions' Guild, which requires you to have 33 quest points.
What You Need: A Wizard's Mind Bomb, Silk, Lobster Pot, an Unfired Bowl, 12,000gp (or 2,000gp if your magic level is 31 or higher with a Wizard's Mind Bomb), an Anti Dragon Shield, 3 Planks, 90 Steel Nails and a Hammer.
Quest Obtained Items: Maze key, Anti-dragon shield, the colored keys, 3 map pieces.
Recommended Items: Good food such as lobsters or swordfish, some decent armour, a few magic or ranged attacks (if you are paying 10,000gp, they are not needed), a weapon and teleport runes if you can teleport.
Requirements
Quest: 33 Quest Points.
Item: 90 Steel Nails [6x Steel Bars] (Members can buy from Sawmill Operator), 3 Planks, Hammer, Lobster Pot, Wizard Mind Bomb, Silk, 2,000gp to buy the Lady Lumbridge, Unfired Clay Bowl, and ONE of the following: 10,000GP OR Runes for Attack Spells and Telekinetic Grab OR Bow, Arrows and Runes for Telekinetic Grab.
Other: Ability to defeat Elvarg (Level-83).
Recommendations
Skill: 50 Attack, 50 Defence, 50 Strength, 25 Prayer, 33 Magic, 34 Smithing, 8 Crafting.
Item: Rune Full Helm, Chain, Platelegs, Scimitar/Long/Battleaxe, Amulet of Power/Strength/Defence/Glory, Gloves or Vambraces (any type), Anti-dragonbreath shield, Any Cape, Strength Potion, Food (Lobster or better), Teleporting Runes, Ring of Life (Members only).
Beginning the Quest
Talk to the Guild Master (in the Champions Guild) and ask about the rune plate. He will refer you to Oziach. Before leaving, use all the options available to you until Dragon Slayer is lit up in your quest listing (i.e. keep talking until you've started the quest). Oziach can be found north-west of Edgeville, just outside of Edgeville. Ask Oziach about the rune plate, then go on to ask him how you can be named a hero. He will tell you that you have to kill a powerful dragon named Elvarg, but the map to Crandor, the dragon's home, was split up into three pieces.
Oziach tells you that you also need an Anti-Dragon Shield. Talk to the Guild Master again. Then, go to Lumbridge Castle; on the second floor is Duke Horacio. Ask him for a shield that will protect you from the dragons breath, and he'll give you one for free. Go back to the Guildmaster and he then tells you where the map pieces are. Make sure you use every option when talking to him. The first map piece is in Melzar's Maze, the Oracle has the second map piece and Wormbrain (a Goblin in Port Sarim jail) has the third. Ask the Guild Master of the Champions Guild about Melzar's Maze and he will give you a Maze Key. You can always get another one back from him if you lose it.
Melzar's Maze
Items needed: Good Magic Defence Armour (Melzar occasionally uses Magic), Fighting Equipment, Food, Maze Key.
Melzar's Maze is located north-west of Rimmington. Use the Maze Key that the Guild Master gave you on the door to get in. From this point onwards, you will need to use different coloured keys to move ahead. Please note you should not leave the maze at any time or else you will need to regain the keys. A map of the doors can be found here. The color of the dot is the color of the door you need to go through.
- Red Key - Kill Zombie rats (Level-3) until you get one. Use the Red Key on the north-west door. Go up the ladder.
- Orange Key - Kill Ghosts (Level-19) until you get one. Use the Orange Key on the second door from the north. Go up the ladder.
- Yellow Key - Kill Skeletons (Level-22) until you get one. Use the Yellow Key on the western-most door. Walk along and around and go down the ladder. Keep going down all the ladders until you reach the Zombies.
- Blue Key - Kill Zombies (Level-24) until you get one. Use the Blue Key on the blue door, NOT the brown one.
- Magenta Key Kill Melzar the Mad (Level-43) until you get one. Melzar the Mad is a mage, so watch out for stun spells. Use the Magenta Key on the magenta door (the northern-most one). If you fear his magic attacks on your metal armour, wear dragonhide.
- Green Key - Kill a Lesser Demon (Level-82) until you get one. Use the Green Key on the green northern door.
- There is a chest in the next room; search it. You will find the map piece.
Climb up the ladder and exit Melzar's Maze.
Oracle's Items and Wormbrain
Speak to the Oracle, south of the Black Knights Fortress on Ice Mountain. The Oracle will tell you that you need four items.
- A drink used by a mage - wizard mind bomb (Falador Pub).
- Worm string changed to sheet - silk (Silk Trader in Al-Kharid, Ardougne Silk Stall, or Varrock Clothes Shop).
- A small crustacean cage - lobster pot (Port Sarim, talk to Gerrant).
- A bowl that has not seen heat - unfired bowl (clay + water = soft clay; Use soft clay on a pottery wheel to make bowl).
Gather the required items before talking to the oracle to save time. When you have all these items go down into the Dwarven Mines (Entrance south of Oracle). 
Head south and then east, and you will come to a room with a chest in it. If you have all four items you can enter by using them on the entrance. Search the chest to get the map piece.
Go to the Port Sarim Jail, just south-west of the boat to Karamja and you will see Wormbrain.
Option 1: This is where the level 33 magic comes into play. You have to Mage/Range Wormbrain and telekinetic grab the Map Piece. Members may use a halberd to kill him if they wish.
Option 2: Or you can buy the map piece from Wormbrain for 10,000gp.
Crandor and Elvarg
Now that you have all three map pieces, put the map together by using the pieces with one another. Go back to the Champion's Guild and speak to the guild master. He will tell you that you must find Klarense. Head to Port Sarim's docks and search for Lady Lumbridge (dock before southern-most dock). Buy the ship from Klarense for 2,000gp. You'll need to use all the options with Klarense as well. You discover that it's damaged; to repair it, you need three planks, 90 steel nails and a hammer.
Go to the bank in Draynor Village and withdraw your supplies to kill Elvarg. Some items you will need include: a strength potion, food (swordfish or lobsters), armour, a one-handed weapon, and an anti-dragon shield. While you're here, tell Ned in a house north of the Bank that you have all the map pieces - he will be waiting for you back at the docks to sail you off to Crandor. Head back to Lady Lumbridge.
When you arrive at Crandor the ship will smash on the rocks. Leave the ship from the bottom level. There are aggressive Skeletons, King scorpions, Hobgoblins, Lesser Demons and Moss Giants on Crandor.
Now make your way to the center of the island and climb down the crevice. Elvarg is found in a cage just by the level 45 Skeletons. Don't linger on the outside, or you might find yourself wasting food. 
Go and push the 'odd looking wall' further south past the Lesser Demons so if you die, you do not need to repair the ship again. You can just sail onto Karamja and go to the dragon's lair through the Karamja volcano.
Open the gate and go in to face Elvarg (Level-83). Once you have defeated Elvarg, pick up her head and bring it to Oziach. To leave go south past the Lesser Demons, and leave via the concealed door. Remember to bring your anti-dragon shield!
Note: If you die the first time during this quest, you don't have to get the planks and nails again. The entrance to the dragon through Karamja will open.
