Accomplish the indicated achievement to get the corresponding number of 
Gamerscore points:

Beginner's Luck - Easy (10 points): Solve the case "Beginner's Luck" on Easy level
Beginner's Luck - Normal (20 points): Solve the case "Beginner's Luck" on Normal level
Beginner's Luck - Hard (30 points): Solve the case "Beginner's Luck" on Hard level
Murder at km 109 - Easy (10 points): Solve the case "Murder at km 109" on Easy level
Murder at km 109 - Normal (20 points): Solve the case "Murder at km 109" on Normal level
Murder at km 109 - Hard (30 points): Solve the case "Murder at km 109" on Hard level
Traffic Control - Easy (10 points): Solve the case "Traffic Control" on Easy level
Traffic Control - Hard (30 points): Solve the case "Traffic Control" on Hard level
A Series of Accidents - Hard (30 points): Solve the case "A Series of Accidents"
Undercover - Easy (10 points): Solve the case "Undercover" on Easy level
Undercover - Normal (20 points): Solve the case "Undercover" on Normal level
Undercover - Hard (30 points): Solve the case "Undercover" on Hard level
Mere Chance - Easy (10 points): Solve the case "Mere Chance" on Easy level
Mere Chance - Normal (20 points): Solve the case "Mere Chance" on Normal level
Mere Chance - Hard (30 points): Solve the case "Mere Chance" on Hard level
Old Friends - Easy (10 points): Solve the case "Old Friends" on Easy level
Old Friends - Normal (20 points): Solve the case "Old Friends" on Normal level
Old Friends - Hard (30 points): Solve the case "Old Friends" on Hard level
The Wager - Easy (10 points): Solve the case "The Wager" on Easy level
The Wager - Normal (20 points): Solve the case "The Wager" on Normal level
The Wager - Hard (30 points): Solve the case "The Wager" on Hard level
Code 9807 - Easy (10 points): Solve the case "Code 9807" on Easy level
Code 9807 - Normal (20 points): Solve the case "Code 9807" on Normal level
Code 9807 - Hard (50 points): Solve the case "Code 9807" on Hard level
Test Driver (50 points): Drive every available vehicle in single player mode
Track Tester (50 points): Drive on every available track in single player mode
Fast (10 points): Drive faster than 220 km/h for 10 seconds in any vehicle
Faster (20 points): Drive faster than 280 km/h for 5 seconds in any vehicle