-( Story related, cannot be missed )-
This is a story-related achievement, therefore you cannot complete the game without getting this. That being said, I have taken the time and effort to write down the steps needed to complete this for you.
*** Spoiler - click to reveal ***Act 1: Sweet Sweet Magic
Part 2a: Business is Booming
After the fight, pick up Abracadaniel and combine him with Jake. Then, use the combined item on the gear to the right of the gate to get in. Once in, show the cake plate to be allowed around the city. A few things to work on getting: the mop and slime in the first screen will be used for your first task. Talk to the Rock Wizard to find your first task in this chapter. After the guard but before the shop will be one street, while the second is past the crowbar vending machine. Head down the first street to pick up the rope, then go to the second and use the rope on the farthest support beam. Pick up the brick, then head back to the first street and work your way around the gnome to use the brick on it. EDIT: To use the brick on him, you'll have to move to the right (away from him) and use Jake to scale the walls. Once on the roof, come back around to the gnome (with the tactical height advantage) and then use the brick from that point. (Thank you, acedawg4, for the clarification.)
Pick up the paint, then return to the first screen. Combine the paint with the mop, then the beard with the slime. You'll be rewarded with a wizard coin and be one-third through the line.
(Suggested break here) You might as well clear out the requirement for the missable achievement, Wrong Number.
What this requires is entering the payphone now next to the magic shop and using the coin to call ten different numbers. You might end up getting some of them on repeat, so just keep using the phone until either the achievement pops or you've properly counted ten different responses (which will possibly prompt that your game may be a bit bugged, but will unlock the achievement at a later time perhaps). (Break's over, back to work!)
Talk to the Wizard Police to find your next task. Using the wizard coin you were given, head to the vending machine and get a crowbar. Return to the second street and use the crowbar on the glowing gem that appeared from dropping the boulder, then return it to the police guy to get the cracked gem. All that's left is Flambo. He'll ask for a restroom, and Ron James's is the only one that's available without a Staff of Relieving. Combine the mop handle with the cracked gem to get a makeshift one. Head to the left and place it in the hole on the ground. But the one we placed is shiny compared to the other, so we have to fix that. With the second coin you got, return to the vending machine and pick up the dusting brush and use that. Return to Flambo afterwards to get your way in.
Part 2b: Party Favors
Inside Ron James's store, you can check out some of the wares including the snail in the left side of the room. Gunter is an object you can pick up, so take him and then return to the second street to go after the bottle. After the fight, pick up the broken bottle. Return to Ron James's shop and speak to the Ice Wizard to find out about the party, but you'll need to bring some snacks. Ron James will inform you of the recycling program he has, but will not accept a half bottle. Exit the shop and you'll see Huntress Wizard beside the shop. She'll give you a bag of chips for a pizza with anchovies, telling you how to do so. The phone number will be found on the bulletin board and you can use the booth, should you have money. Head back to the first street to encounter some gnomes after Rock Wizard's beard. Stop them to retrieve a broken bottle piece, then combine the two pieces together to get a complete bottle. Head back to Ron James's shop and trade him the bottle for a coin.
Use Sassy's Pizza flyer with the phone booth to get three pizzas, one with anchovies. You'll also get the chance to get the hooked stick from the delivery candy being turned. Give the pizza to Huntress to get the bag of chips, but Ice King will not be entirely satisfied with the offering of pizza and chips. Head outside, back to the vending machine, to find that it is offering a drink now. Use the last coin you have on it only to watch it get snagged. This is where the hooked stick comes in handy. With all three items gathered, return back to Ice King and give him the goodies to get in to the party.