The quest that takes you to Krokotopia is named Krokotopia. No really, it is. Do that quest and it takes you to Krokotopia. After completing the three areas that link from Olde Town, you get the quest line:
A Look of Horror -> The Dark of Nightshade -> The Sixth School -> Krokotopia -> (more quests in Krokotopia itself)
To travel the whole spiral and all the worlds you have to follow the main quest. At the end of each world the headmaster will grant you the key to the next world.
Check your quests. You actually don't have to do Collosus to travel the spiral.
Look for a quest where the Headmaster sends you off to get a key (in Olde Town tower); then to fight Lord Nightshade (Haunted Cave tower); then to explore the door behind the waterfall....
Not necessarily in order and exact...but that is the quest that gets you the key to the spiral.
