One of the faster ways is to use the Port Sarim lodestone and run a short ways northwest to the White Knight Camp and enter the cave. Then run west down the tunnel and enter the shortcut to the south (Requires 50 Agility). After that, the entrance to her lair is just south of you. Graves spawn just outside of it

When doing the kill, the recommended style is Range for learners, and melee or mage once a bit more experienced.

Suggested Inventory

Searing Overload, Replenishment, super restores or prayer potions, prayer renewal, enhanced excalibur for easy heals, portent of life, and rocktails. If you bring a beast of burden, fill that with food as well, but it's suggested to use a combat familiar such as a steel titan or shadow nihil.

Range

Head: Slayer Helm (on task) > Sirenic > Pernix
Necklace: Souls (for speedkills) > Farsight Sniper > Blood Fury
Cape: Completionist > Tokhaar Kal > Max > Ava's Alerter
Body: Sirenic > Pernix > Armadyl
Legs: Sirenic > Pernix > Armadyl
Weapon: Nox Bow / Ascensions > Royal > Attuned Crystal
Ammo: Araxyte Arrows / Ascension Bolts > Dragonbane > Royal
Boots: Flarefrost (not worth the money unless doing speedkills) > Pernix > Armadyl
Gloves: Dragon Slayer (On task) > Ascension (speedkills) > Pernix > Armadyl
Ring: Ring of Death > Asylum Surgeon's > Archer's (i) > Sixth Age Circuit


Melee

Head: Slayer Helm (on task) > Malevolent > Torva
Necklace: Amulet of souls (speedkills) > Brawler's Knockout > Blood Fury
Cape: Completionist > Tokhaar Kal > Max > Fire Cape
Body: Malevolent > Torva > Bandos
Legs: Malevolent > Torva > Bandos
Weapon: Scythe > Drygores > Attuned Crystal Halberd
Ammo: Prif Quiver to reduce prayer drain
Boots: Emberkeen (tryhards) > Torva > Bandos
Gloves: Dragon Slayer (on task) > Torva > Bandos
Ring: Ring of Death > Asylum Surgeon's > Warrior (i) >Sixth Age Circuit

Mage

Head: Slayer Helm (on task) > Tectonic > Virtus > Subjugation
Necklace: Souls (speedkills) > Arcane Stream > Blood Fury
Cape: Comp > Tokhaar Kal > Max
Body: Tectonic > Virtus > Subjugation
Legs: Tectonic > Virtus > Subjugation
Weapon: Nox Staff / Seismics > Seasinger Kiba > Cywir Elders > Attuned Crystal
Boots: Hailfire (tryhards) > Virtus > Subjugation
Gloves: Dragon Slayer (on task) > Virtus > Subjugation
Ring: Ring of Death > Asylum Surgeon's > Circuit
 

When you first start the kill, you have a few seconds to drink potions and get ready while she wakes up. Once she is awake there will be a health bar at the top, showing the health she has left in her current phase. There are 4 phases, and after each one you have to tag an ancient artefact that will only activate when she is out of health. For rangers, it is best to stand on the square west of the ancient artefact on solid ground so there is a chance to get a gap in a firewall without moving, and so you can immediately tag the artefact after the first phase ends. You must tag the artefacts in order: the first artefact after phase 1, the 2nd after phase 2, the 3rd after phase 3, and the 4th after phase 4 to end the kill and collect your loot. Between phases when you have to tag the artefacts, the Queen will cough up small grotworms that will attack you for the rest of the kill. They don't hit very hard, but if you take a lot of time tagging the artefacts they will add up and can severely drain your health. Here is a picture of the start of the kill indicating where to stand, and where the artefacts are located at.
At the start of the kill you won't be able to access the last 3 artefacts. After each phase, a magical surface will appear giving you room to tag the next artefact, but do not stand on them. Standing too long on the surface will result in a hit of 1500 hp, and you will keep being hit for that every few seconds until you return to the solid ground so tag the artefacts and run back to her to continue the kill.

Special Attacks

Firewalls

Firewalls spread across the entire solid platform and move from north to south, with 1 open spot appearing in 1 of 3 places in each wall. Standing on the spot west of the 1st artefact means you have a chance of standing in one of these gaps. If you are hit by the firewall, you are hit for 750 damage every couple ticks if you are on super antifire.

Tortured Souls

Tortured Souls are occasionally spawned by QBD after phase 1 and have 2000 hp. In phase 2 she can summon 1 at a time, 2 phase 3, and 4 in phase 4. After spawning, each one will release a slow moving chaotic cloud that hits up to 1200. You can move around and drag the cloud into other Tortured Souls and grotworms so that they are hit instead. Tortured Souls can also stop time. This can happen when one teleports to the edge of the arena and shouts "Kill me mortal...Quickly!" but this can be avoided by killing the souls. If you do get stopped in time, you will be unable to move, eat, or teleport but QBD will continue to attack. After time resumes, all hits that you took while stopped will be combined into 1 attack that easily kill you, so kill the souls as soon as they appear.

Extreme Dragon Breath

On Phase 4, QBD can use her Dickbreath attack, a very powerful form of her dragonbreath attack. Being in the middle will give you hits of 1950 damage every couple of ticks, and being on the side will give you hits of 750 damage. This is the attack required to forge the Royal Crossbow.

Carapace Form

On phases 3 and 4 QBD can enter a Carapace Form lasting for 1 minute where she takes 25% more damage from magic and 25% less from melee and ranged. She will revert back to normal at the end of the phase.

Crystalline Form

On phases 3 and 4 QBD can enter a Crystal Form for 1 minute where she takes 25% more damage from melee and ranged, and 25% less from magic. She will revert back to normal at the end of the phase.

Phase 1
Phase 1 is the most basic part of the kill, where you don't have to worry about any special attacks except for a possible firewall.

Phase 2
QBD can now summon 1 Tortured Soul at a time, and can send out 2 firewalls.

Phase 3
QBD can summon 2 souls at a time, send out 3 firewalls, and can use either Carapace or Crystal form.

Phase 4
QBD can summon 4 souls at a time, send out 4 firewalls, can use Carapace or Crystal forms, and can use Extreme Dragon Breath.

Looting
After you touch the final artefact, all grotworms and tortured souls will die, and QBD will return to her slumber. A door will open up under the first artefact and you can go down them to loot the Dragonkin coffer in the room below. After that you can use the door portal to either quick start another kill or leave the instance.