Here is the full list of all 14 Delicious - there are Emilys Message in a Bottle achievements.
Finished Emilia's Place Restaurant
Complete all the levels at the Emily's Garden restaurant
Complete all the levels at the Old Family Restaurant
Complete all the levels at Marco's Fish Market
Complete all the levels at Gino's Farm
Complete all the levels from Vinicio's Vineyard
Complete all the levels from the new Napoli Family Restaurant
Complete all the levels on the Hippie Island
Find all the mice across every level of the game
Achieve 3 stars on every level
Unlock all the menu upgrades across all chapters
Buy every product from every store
Collect all the memorable moments in the game
Use all the diamonds to unlock every family character