Cook's Assistant, Desert Treasure, Fishing Contest, Goblin Diplomacy, Big Chompy Bird Hunting, Biohazard, Demon Slayer, Murder Mystery, Nature Spirit, Priest in Peril, Restless Ghost, The, Witch's House, Gertrude's Cat, Shadow of the Storm, Lost City, Monkey Madness, Horror From The Deep, and started Legends' Quest= These are the quest requirements.
So if we add that all up we get:
53 thieving
50 firemaking
10 slayer
10 fishin
30 ranged
5 fletching
50 woodcutting
50 crafting
45 herblore
50 agility
56 magic
42 prayer (im not sure about this ill try to find the quest again and correct but u probally dont need the 42prayer)
50smithing
52mining
70 cooking
This requirements assume that you have completed legend's quests, altough you don't really need to have them to start it. In my opinion, might aswell finish the quest as it gives some pretty handy rewards.