In theory, you should obtain this achievement by solving all the Observations in the game but various people didn't get it even following guides on the web. Because of that, I decided to list all the things I observed (glasses icon) during the playthrough that finally granted me the achievement, even if most of them shouldn't count towards it. Follow the list order or you'll easily miss at least a couple of Observations.
If you have any question or suggestion, leave a comment below!

Outside

• Japp
  
• Fruit and Vegetables shop on the right
  
• Empty shop on the left

Shop

• Shelves and newspapers on the right
  
• Counter
  
• Shelf behind counter
  
• Alice's body

Back of the shop

• Bed
  
• Mirror
  
• Stoves
  
• Inside locked chest

Outside

• Nancy Bodley
  
• Vinegar bottle

Back of the shop

• Alice's neice

Shop

• Shelf knocked over by Franz
  
• Franz

• Newspaper
  
• Hastings
  
• Cabinet with two lamps
  
• Mirror

• Medals board
  
• Hastings
  
• Interview room door
  
• Map
  
• Japp

Beach

• Policemen on the right
  
• Hastings
  
• All 5 cabins
  
• Body
  
• Sea
  
• Victim's cabin
  
• Building on the left
  
• Newspaper kiosk

Restaurant

• Table
  
• Hastings
  
• Jukebox
  
• Restaurant owner
  
• Mirror
  
• Counter
  
• Hastings again

Betty's home - downstairs

• Piano
  
• Betty's sister
  
• Mirror
  
• Gramophone
  
• Cabinet

Betty's home - upstairs

• Mirror
  
• Music stuff
  
• Clothes on bed
  
• Box of stockings
  
• Invitations
  
• Clock
  
• Record sleeve on wall
  
• Left night stand

Betty's home - downstairs

• Betty's sister (Falcon's eye should unlock here. If it doesn't, you missed something.)

Restaurant

• Donald Fraser
  
• Hastings

• Mirror
  
• Cabinet on the left
  
• Newspapers
  
• Cabinet with two lamps
  
• Suitcases (say to Hastings that order is essential or you'll miss it)
  
• Hastings

Outside

• Bush on the left
  
• Rock with seagull
  
• Carmichael's body
  
• Blue cloth
  
• Trampled grass below bush

Inside

• Hastings
  
• Carmichael's brother (observe him before her or you'll miss it)
  
• Thora Grey
  
• Table
  
• Both glass cabinets
  
• Map
  
• Golden dragon
  
• Portrait above golden dragon
  
• Locked cabinet with lamp
  
• Bookshelf
  
• Hastings again
  
• Thora Grey Again

• Hastings and Franklin Clarke
  
• Thora Grey and Mary Drower
  
• Donald Fraser
  
• Megan Bernard

Downstairs

• Mirror
  
• Lioness head 1/2

Upstairs

• Lady Clarke

Downstairs

• Lioness head 2/2

Upstairs

• Mirror 1/2
  
• Lady Clarke again, after she falls asleep
  
• Mirror 2/2
  
• Night stand
  
• Pictures on cabinet

Downstairs

• Blue trunk
  
• Dresser

Living room

• Golden dragon
  
• Locked cabinet with lamp
  
• Bookshelf
  
• Book on round table
  
• Both glass cabinets
  
• Map
  
• Papers on table

Study

• Bear head
  
• Antelope head
  
• Shelves with tennis rackets
  
• Chinese chest
  
• Map

Garden

• Vase out of place on the right
  
• Fountain
  
• Arbor
  
• Right side of the garden
  
• Wheelbarrow
  
• Greenhouse

Cliff

• Cross

Befare talking to Fraser

• Mirror
  
• Cabinet on the left
  
• Newspapers
  
• Bottle on the table
  
• Donald Fraser

Before calling Japp

• Mirror again
  
• Cabinet with lamps
  
• Newspapers again
  
• Cabinet on the left again

After calling Japp

• Reconstructed documents

Outside

• Prices board
  
• Window

Inside

• Piano
  
• Cushion on counter

After talking with Miss Marbury

• Mrs Marbury while she's peeling potatoes
  
• Register on counter

Cust's room

• Mirror
  
• Floor near sink
  
• Shelf with medicine bottles
  
• Wardrobe
  
• Bed
  
• Document on wall
  
• Desk
  
• Boxes on floor

Downstrairs

• Japp

• Cust (Eagle's eye should unlock here. If it doesn't, you missed something.)