Complete the objective on every board to move to the next one. You don't need to win any minigame, nor do you need more than 0 score to buy items from the shop. The game will end the same way regardless of whether you're first or last at that point.

Visiting the shop: If you have a Sale Flyer in your inventory you can enter the shop. You can only enter the shop while other players are duelling - on the bet screen touch the shopping cart to enter it. There is no way of exiting it other than waiting for the other players.

You can soft reset the game by pressing L+R+Select+Start, which lets you restart the current board.

Specific level requirements and tips: Port Town - Get to the end, avoid cage spaces and boats near the end. Desert - Find all 4 Key Items, it can be any player and they can only be found on grey (neutral) spaces. Key Items may spawn on the second map, in which case you need to stand on the spaces with feathers next to them to enter it (or use an item). Big City - Find all 4 Key Items, same deal, although you might need to flip a square using the Spatula (or equivalent). This is where you should use a Magnifying Glass to see the Key Item locations. Volcano - Get to the top of the volcano, some grey spaces throw a rock at you, tap on them to see which ones do. Deep Sea - Find all 4 Key Items, you will need to flip over spaces and check the locations just like in Big City. There's 2 additional side maps on this board. Tower - Get to the top of the tower, there's a second floor which you can teleport to using an item, the knight statues will almost always knock you out of the tower if you stand on their spaces.