You need to complete all the listed quests AND defeat Araxia in the final fight.
1 - Viva Repugia! - Gained by walking past the Grubbin behind the 'Revolution' Stall - Visit 20 Houses
2 - Hook, Line & Freethinker - You gain this quest by talking to the grubbin leader, who is in the 'Secret Cave' just east of where you are pushed off the cliff. - Talk to the grubbins in town to find the 3 materials.
3 - Grubbin Lovin' - Given to you by the grubbin guard, near the Monster gate, on the east side of town - Talk to the elder (Who is just north of the bridge) about getting through the gate. Then go rescue his ladyfriend who is in the hotel. To get to her, you need to use the zip line that is next to the gate that you got this quest originally, then use the Fry costume to lure her up the ramp and off the drop, back to the elder.
4 - Tome of the Trowbogs - This mission is to get the next gate open. The tomb is found west, right next to the gate.
5 - The Case of the Missing Yeti - This is to open the third gate (Crestwailers gate). You need to find out where the yeti has gone. You will eventually run into a crestwailer who will give you the costume for the Yeti. You need to simply exit the cave, head south a little so you are at the ledge and it will show a little cutscene. After that, return to the leader, who is eastwards.
6 - Save The Escapees - You can gain this quest by talking to any of the hiding kids, use my guide here for help on their locations. The earliest kid is just south of the first bridge, within the maze area. 6 kids to find in total.
7 - Bobbing for Eyeballs - Beat the 3 tiers of the Bobbing for Eyeballs minigame.
8 - This Card is Ultra Rare - Gain an extra care to trade.
9 - Repugia Collect 'em All - Gain an extra card to trade.