Here's a step by step play of Chapter 5 Looker sidequests:
1) Get to the black building next to the museum; it's the hotel (on north Blvd)
2) Go up the elevator to 5F
3) Find Malva and battle her (south and onto the room on the left)
4) After listening to her story, head to Lysandre Cafe; prepare for battles (near Magenta Plaza)
5) Malva will be waiting for you to take you to a hidden room
6) She will take you to an elevator - go to the "Hidden Floor"
7) When reaching there, you will battle a scientist. From there, take the left arrow immidiately from the scientist and go into the green warp circle.
8) After, you will battle another scientist. Then, go on the arrow south of the scientist, followed by another arrow south of where you end up. After, go east on step on the arrow pointing to the right. Finally, step on another arrow also pointing to the right - this will take you to Lumiose Gang Member Sedna.
9) After the battle, go to the arrow left of Sedna. Then, go southwest where you will end up battling Gang Member Eris.
10) Then, step on the green circle left of Eris - this will take you to Scientist Justus.
11) After, step on the green circle near Justus - this will take you to Gang Member Nix.
12) After this battle, Nix takes you to a room (collect the pokeballs stolen from trainers).
13) Then, go to all the bookshelves and read each volume and stories (there's some down the stairs)
14) Talk to the punk after, and he will leave his shift as you replace it
15) You will be taken into battles (pretty straight forward from here). You will need to battle Essentia several times.
16) Afterwards, Mimi comes with Espurr and takes you back to the office
17) After some talking, you will complete the quest.
If you found this was complicated, maybe this video will help you.
Hope I helped! :)