Anti-Guy, the super powerful Shy Guy found in Shy Guy's Toy Box, can be a very difficult fight. To skip fighting him and get the chest he is guarding (containing an attack power+ badge), you can bring him a Lemon Candy. Talk to him and he'll ask if he can have it, and if you say yes, he'll take it and run off. He'll never come back, so you'll lose any XP you would have normally gained by fighting him.
A Lemon Candy can be made with a Lemon and Cake Mix. The Lemon can be found in the Dry Dry Desert level. Bring them to Tayce T in the main town and she'll make one for you.