Head down to South/North Boulevards and you should get another request from Looker for another case to solve: head into the bureau. He'll tell you to read the notebook on his desk for notes concerning the case: basically, the kids of the city like to play in the alleys, and the parents are worried and suspicious.
Speak to Looker and he'll tell you to start your search in the alleys leading from South Boulevard. Okay, time to get going! Head along to South Boulevard, specifically the Route 4 gateway. Head clockwise along the northern side of the street and you'll find a sleeping Skiddo next to Restaurant Le Nah: enter the nearby alleyway.
Within, you can progress northward as long as you do battles on the way. Careful, the kids inside are weally, weally strong! (Well, stronger than the average preschoolers - what parents allow their kids to have such powerful Pokémon, easily capable of lasting through the sixth Gym at least ?)
Trainer Battle: Preschooler Natalie
Trainer Battle: Preschooler Lily
Trainer Battle: Schoolgirl Callie
Trainer Battle: Schoolboy Macon
Survive the gauntlet of children and Looker will rush in ahead of you, ready to probe the alley's depths. At this point, an Espurr pounces forward, rather angry at having its territory intruded upon. Following the Espurr is a mysterious girl, who explains why she and the other kids are hanging around the alleys.
Just when Looker has a solution for their predicament, the Espurr - Mimi - runs off. Your next task is to go find and befriend the little critter. According to Looker (as you exit the alley), Mimi probably ran off to one of its usual haunts. To be precise: across from the Galette Stand, across from Lumiose Station or right next to Cafe Triste.
All three locations are alleys found in North Boulevard . The first is opposite and a bit to the left from the Galette Stand, between the Route 13 and 14 gatehouses. The second is opposite Lumiose Station, a little clockwise from the Route 16 gatehouse. Finally, the third alley is to the right of Cafe Triste, where a woman is standing nearby.
When you enter an alley, be sure to go to the very end - head west and if you find Mimi, sing to it . Mimi will run off and you'll need to find it again in one of the other two alleys. After you've sung to Mimi three times , you'll automatically be brought back to Looker and Emma, and the chapter come to a close.