In chapter 3, theres a dress up kit in the living room with 12 accessories in it.
Diamond collar, Bow-tie, Spiked collar, Bandana.
Tiara, Top hat, Fez, Sailor hat.
Movie star glasses, Heart glasses, Pince-nez glasses, Trendy glasses.
Two of the items require unlocked, the Sailor hat and the Trendy glasses.
To unlock these, Go out the window and to the town, get the fashion magazine from the stall, then make the Constable question the Major. Follow him to the kitchen and take the Sailor hat when he puts it down. Give both to Felicity at the Dress-up kit.
After dressing the dogs with all 12 accessories (3 at a time) the achievement will unlock.