Lost Judgment

You get access to the dog (Ranpo, a good boy) late in Chapter 4. What the game counts as 'targets' isn't clear, but I think what counts is:

• clues or people Ranpo sniffs out as part of side cases
• Squirrel Search items

What don’t seem to count towards the achievement are:

• the five unique items Ranpo finds (four in Yokohama and one in Kamurocho)
• materials (white cube icon) and items (white glowing orb with blue arrow) he randomly finds in the street

Here are all the squirrel searches that involve using Ranpo:

Yokohama

• On the little river walk southwest of the Batting Center, near the water
• Next to the Carriage Highway Taxi Stand
• West along the wall from the Jinnai Station Poppo (Interior) (#1, Noise Amp), on the courthouse steps (#2, detector), on the notice board (#3, Ranpo)
• North of Coming Boon, in the tiles on the sidewalk
• On a tree north of the Hamakita Park Ave. sky bridge
• South of the Hello Work Taxi, on the south wall
• On the east wall in Ijin St.

Kamurocho

• To the east of the Theater Square Club SEGA, left of NY Hot Dog
• As you enter the Champion District from the west, on a wall (#1, Noise Amp), north side of the Champion District, on a bar wall (#2, Detector), on a set of stairs in the centre of the district (#3, Ranpo)
• In Tenkaichi Alley, on the east side of the Jungle Boy wall
• In the tiny lot to the east of Sushi Zanmai
• On the ground in front of the Tenkaichi St. entrance
• On the ground across from Ebisu Pawn (#1, Noise Amp), In the alley near Ebisu Pawn (#2, Ranpo)

Information compiled from CyricZ's indispensable GameFAQs guide (which includes maps of the above):
https://gamefaqs.gamespot.com/ps4/320117-lost-judgment/faqs/...