You can find this sidequest in "Capitol D. City - Capitol D. City". You have to collect 3 items. After you accept a quest (look at the map for seeing a weird-looking icon as a level icon, to spot the side quest) you will see the quest icon by 3 missions. When you go to a mission with a sidequest you can press Y on a gamepad to get to that side quest. This means you have to beat a level with specifically selected dogs, those may not always be your favorite type, but it should be very doable, if not level up one of those dogs you use the most in that sidequest.