Taiko no Tatsujin: The Drum Master!

Items in the shop are random and rotate daily (at 5AM your time zone). You can either reroll the store for 1,000 coins or wait until the needed items show up - the Pizza head for 800 coins and Cheeseburger body for 800 coins - to purchase them. Once you have them, equip them to your avatar and play any song. You can even opt to put the Perfect modifier on in the options before selecting a song to fail out, saving time. After viewing the results, the achievement should pop.

If you want to save any coins spent, such as rerolling and purchasing the cosmetics, instead of closing the game out normally, delete the local save. That will get you back to any amount of coins saved prior - if you want to make sure your game is saved before purchase, close out the game and restart it. Please note: this is not a method of my personal experience; I'm buying to collect all the items and this will remove the items from your collection if you technically 'reset' your save after triggering the achievement. Posts on the forum for this game are pretty helpful with this method, if you need further clarification.