Initiating the Quest
You can initiate the quest by speaking with Arwen in Ellinia. Accept the quest after hearing her story. Her description of the monsters that took her glass slippers is vague, but she provides two important clues in her story to help you deduce where to start looking for the culprits. She says the monsters were covered in fire and that she was attacked outside of Pieron. From this you should deduce that the monsters are fire boars from the Burnt Land, directly outside Pieron. Follow the signs from Ellinia to the Burnt Land to find the fire boars.
Fire Boars
Fire boars are a formidable foe in "Maplestory." Your character should be at least level 25 before attempting to complete this quest, otherwise you'll have a difficult time trying to kill a single fire boar, let alone several dozen. Fire boars are scattered throughout the Burnt Land in the Burning Heat and Ash Covered Land areas. The boars' weakness is ice; attacking them with a weapon that deals out ice damage will make killing them much easier.
Purchasing the Glass Slippers
The glass shoe randomly drops after killing a fire boar. This means you could receive a glass shoe after killing your first fire boar or you'll receive your first after killing your twentieth. As a result, for some this quest takes minutes and for others it could take days. Instead of wasting hours killing boars in hopes that they'll drop a glass shoe, kill enough boars to gather loot worth 250 mesos, which is the value of a glass shoe. If a glass shoe falls in that time great, if it doesn't move on to Plan B. Sell the loot collected from the fire boars at any town trading post. Travel to the free market and look for a player selling glass shoes. Purchase a glass shoe for 250 mesos. Alternatively, skip killing any fire boars and purchase a glass shoe from the free market immediately if you have the coin to spare.
Ligators
Glass shoes aren't limited to fire boars; ligators also randomly drop glass shoes. Ligators are located at Wild Crocodile Swamp and Dangerous Croco in the Swamp Region. A ligator is far easier to kill than a fire boar. Attack a ligator with a weapon capable of doing fire damage, a ligator's weakness, to make killing a ligator far easier. Search for glass shoes amongst ligators if your character is below level 25, but at least level 20. Going this route will allow you to complete the quest with a lower level character than what's recommended.