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

Everybody Starts Somewhere (10 points): Buy your first property.
Now You're On Your Way (20 points): Own your first monopoly.
Climbing Your Way Up The Ladder (30 points): Build your first set of houses. Classic mode only.
The View From The Top (50 points): Build your first set of hotels. Classic mode only.
High Roller (10 points): Roll a double six.
Rolled To Jail (10 points): Roll three doubles in a row and get sent to jail.
Rolled To Freedom (10 points): Rolled a double to get out of jail.
Globe Trotter (50 points): Land on every property on the World board.
Taking Sides (50 points): Own every property, including any ports and utilities, down one whole side of the board.
Transport King (20 points): Own the monopoly on the transport properties.
You've Got The Power (20 points): Own the monopoly on the utilities.
Deal Of The Century (20 points): Form a monopoly as a result of trading.
No Mercy (20 points): Be responsible for the bankruptcy of another player.
Went For Broke (10 points): Bankrupted yourself out of the game for the first time.
A Good Start (10 points): Win your first mini-game in any mode of Richest.
He Who Controls The Dice... (50 points): Win every mini-game in a full game of Developer.
Last But Not Least (20 points): Win all the mini-games in a full game of Developer but don't finish first.
Taken A Chance (10 points): Take your first property from another player using Chance in any mode of Richest.
Forcibly Formed (20 points): Form a monopoly in any mode of Richest by taking one or more of the properties from another player.
Dashed Hopes (10 points): Break up another player's Monopoly.
A Quick Victory (10 points): Win a game of Developer mode Richest.
Faster Better (20 points): Win a game of Industrialist mode Richest.
Becoming The Master (40 points): Win a game of Tycoon mode Richest.
The Underdog (50 points): Don't finish first in any mini-game but still win overall in any mode of Richest.
From The Flames (50 points): Come from last in the previous round to win overall in any mode of Richest.
You Are The Richest (100 points): Own every property on the board in any mode of Richest.
Started Your Empire (30 points): Build a set of houses in any mode of Richest.
Established Your Hold (50 points): Build a set of hotels in any mode of Richest.
Time To Collect (10 points): Collect your first rent payment from any other player in any mode of Richest.
Expensive To Stop Here (10 points): Land on another player's set of hotels in any mode of Richest.
Sight Seer (20 points): Unlock a passport. Awarded to the passport holder.
Jet Setter (100 points): Fill all the passports. Awarded to the passport holder.
Try Something New (10 points): Unlock your first new board.
The First Monopoly (50 points): Get the same amount of money as the year Monopoly was released.