Teleport to Lunar Isle from the second page of city teleports and run north to find the Foxtail.
Rat Poison is found outside the Draynor Manor. Teleport to Lumbridge from the city teleports and run northwest to the Draynor Manor, look for the quest symbol.
After you are at the gate, travel west, to the north of the wall, until you reach the fountain. Search the fountain to find rat poison.
Head to Varrock through the city teleports and run northeast to find the Varrock Museum. Search the display cases to find the Angels Heart.
COMPLETING THE QUEST! - Simply return to the mercenary adventurer with all the above items and he will take them from you with some dialogue, after which he will offer you the option to tele to his minigame.
Three styles of Gear is recommended but not needed, one will suffice. Regeneration potions make this dungeon much easier, it is almost a requirement but can be completed without.
Walkthrough of the Dungeon
Once you are geared up and have your three combat styles, ensure you are on the elemental magic book. (Normal magic book)
Grab an overload and have one sip, heal at home then enter the dungeon by talking to the Mercenary Adventurer.
The Dungeon Guardian
You begin in the start room with several cooked slimy eels and a weakening potion. The Dungeon Guardian is blocking your path so start attacking him and use your weakening potion on him to deal serious damage!
Once you slay the Dungeon Guardian he will drop Bravery Potions. These heal you to full HP, prayer and work similar to extreme potions by boosting your stats to 117 and slowly wear off.
Head west and you will find Chaos Dwarves. These guys drop cooked eels (food), vials or water (for anti-poison) and lockpicks.
Lockpicks can be used to open Closed Chests that are scattered throughout the dungeon to give you food and buff items.
Now, let's continue on in the dungeon to the first boss. You will need to use all 3 styles as indicated in the chatbox. While you are fighting you will see in the chatbox "The boss is now weak to melee attacks" or mage attacks or range attacks and you need to change your style accordingly.
Head west from the starting room to find the boss Plane-Freezer Lakhrahnaz
Change styles and watch your health when minions spawn at 90% HP!
The boss will drop a stun scroll which is used for the next phase of the dungeon.
The Three Wizards
Head north of the first boss to a room full of wizards.
Kill the wizards to get elemental runes and one set of infernal ashes. Gather around 300-400 of each elemental room then head north to the room filled with a Water Wizard, Fire Wizard and Earth Wizard.
You need to use:
Earth wave on the Water wizard
Fire Wave on the Earth Wizard
Water Wave on the Fire Wizard
I like to head Northeast and single out the water wizard first then fight the other two.
After you kill all 3 wizards, loot the chest in the center of the room to receive 4 Maxhit potions, which increase your maximum hit by 40 for 45 seconds, and a task list.
The Giant Skeleton
Head to the east, along the northernmost trail, past several chaos dwarves until you reach a pack of skeletons. Follow the trail north past them to find the Giant Skeleton.
Kill the skeleton to receive two more bravery potions and more importantly, the use of prayer!
Head south of the giant skeleton to find regular skeletons which you should kill to get Blindweed.
The Boss Guardians
Follow the path south of the gate first to the end to find a Boss Guardian wizard. Kill the boss and pick up the Godmode potion he drops. Then, travel north of the gate and find the second Boss Guardian at the end of the northern trail. Defeat him as well and grab the Godmode Potion.
*CAUTION* If the Boss Guardian poisons you, use the Cure Magical Potion to alleviate the poison. Otherwise you will receive constant damage for the rest of the dungeon!
Now that you have defeated both of the Boss Guardians, it's time for the final Boss!
The Last Fight
How the Boss attacks:
During the first phase and start of the second phase you will need to prayer switch based on the attack he uses. You will have a second or two to switch which is plenty of time but if you miss then on hard mode he hits up to 90!
Here is what the attack looks like when you should pray Deflect Range.
Here is what the attack looks like when you should pray Deflect Mage.