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

Winner! (10 points): Win one game of Boggle.
Loads Of Winning! (30 points): Win a total of 5 games of Boggle - Any mode.
Wordsmith (20 points): Score 5 6-letter words in one round of Boggle.
Bits and Pieces (10 points): Make 10 words that are 3 letters long in one round.
Portal Pro (20 points): Win 10 games of Boggle with Portal Cubes turned on.
The Mind Boggles (20 points): Win a game with 20 words that are 3 letters long.
The Mighty 8 (20 points): Spell an 8-letter word in Boggle.
I Call Fives (20 points): Finish a game only using 5-letter words.
Fifty Wins (40 points): Win 50 multiplayer games of Boggle.
You are Win! (10 points): Win just one game of Connect 4.
More Wins! (20 points): Win a total of 10 games of Connect 4.
High Five (20 points): Win at Connect 4 by connecting 5.
Grid Lock (20 points): Finish a game with a draw by filling the whole board.
Smooth Operator (20 points): Connect 4 in under 2 minutes.
Operator, this is an emergency (20 points): Connect 4 in under 30 seconds.
Power Chip Collector (20 points): Win a game of Connect 4 Using all of the Power Chip types at least once.
Horizon Line (20 points): Win a game of connect 4 with a horizontal line of 7 pieces. Single player or multiplayer.
Lord of the Wins (30 points): Win 50 games of Connect 4.
Perfection (20 points): Win 4 single player rounds in a row!
Win! (10 points): Win one game of Sorry!
5 Times Win! (25 points): Win a total of 5 games of Sorry! against a friend.
My Apologies (5 points): Move one pawn of an opposing team back to the start zone.
Fragile Alliance (10 points): Finish Sorry! without sending any of one teams pawns back to the start.
I am not Sorry at all (30 points): Win a multiplayer game in under 10 minutes.
All Out Offensive (30 points): Move 2 pawns from every opposing team back to the start in one game.
Rainbow Dancing (10 points): Win a game after moving one pawn from each team back to the start zone.
The Yellow Dart (20 points): Use a Sorry! yellow slide to send a pawn back to start.
Red Vengeance (20 points): Use Sorry! on an opponent within one round of them using Sorry! on one of your pawns.
Master of the Cards (40 points): Use all the Sorry! Bonus Cards in one game.
For the Win! (10 points): Win one game of Yahtzee against a friend.
All the Sixes (20 points): Get a Yahtzee with all sixes!
High Chance (25 points): Fill the chance Total with a score above 24.
Dice Time (20 points): Clock up over an Hour of playtime in Yahtzee.
High Roller (15 points): Roll 3 Yahtzee's in one game.
Real Small (20 points): Roll a small straight starting with a 1.
I Only Need One... (30 points): Roll a Yahtzee, Full House or Large Straight on your first roll.
Ground Floor Apartment (10 points): Roll a Full House using only 1's and 2's .
Infinite Win (40 points): Win 50 games of Yahtzee.
Winningtons! (10 points): Win one game of Sorry! Sliders.
So Many Wins... (20 points): Win 20 games of Sorry! Sliders.
Flawless Victory! (20 points): Win a game of Sorry! Sliders without losing a Slider off the board.
Battle Box Master (20 points): Finish a game having used all of the powerups at least once.
Fast Sliding (10 points): Win at Sorry! Sliders in under 5 minutes.
I Don't Need Help (10 points): Finish one game with Battleboxes turned on but do not collect a single one.
Over the falls (30 points): Knock 4 pawns of the same colour out in one game of Sorry! Sliders.
Slide Time (30 points): Play Sorry! Sliders for a total time of 1 hour.
Ice Man (20 points): Use the Ice Pawn 10 times .
Event Horizon (30 points): Win a game of Sorry! Sliders on Instant Sorry without falling into the centre hole.
Captain Win! (10 points): Win one game of Battleship against a friend.
Destroyer'd! (20 points): Sink your opponent's Destroyer before any other ship.
Make Every Shot Count (20 points): Sink a ship longer than 3 units without missing.
The hunt for Blue November (20 points): Win a game of Battleship Salvo with your submarine still afloat.
Beginners Luck (10 points): Score a hit on your first turn.
Escort Mission (30 points): Finish a game with two ships still afloat that are next to each other.
Sea Commander (30 points): Win 20 games of Battleship.
Iron Bottom Sound (30 points): Sink all your opponent's ships in Salvo Mode within 4 turns.
Minimal Loss (20 points): Win at Battleship while keeping at least 3 of your fleet afloat.
I thought I heard singing... (10 points): Do not fall for a Decoy.
Word Win! (10 points): Win one game of Scrabble. (Scrabble is only available in the North America and UK regions).
More Winning (20 points): Win 5 games of Scrabble - Any mode. (Scrabble is only available in the North America and UK regions).
Cleaned Out (20 points): Use all of your letters on one turn. (Scrabble is only available in the North America and UK regions).
World Wide Web (20 points): Complete one game of Scrabble on Xbox LIVE. (Scrabble is only available in the North America and UK regions).
Bridge the gap (20 points): Reach the other side of the board in bridge builders. (Scrabble is only available in the North America and UK regions).
A column of 7 (20 points): Place 5+ tiles in one go to create a vertical 7 letter word. (Scrabble is only available in the North America and UK regions).
Fire it up! (10 points): Spell 5 words with letters that are "on fire". (Scrabble is only available in the North America and UK regions).
Lengthy Word (20 points): Place 5+ tiles in one go to create a 9 letter word. (Scrabble is only available in the North America and UK regions).
Captain of the Scrabble Team (30 points): Win 20 games of Scrabble. (Scrabble is only available in the North America and UK regions).
Take your time (30 points): Reach over an hour's playtime in Scrabble. (Scrabble is only available in the North America and UK regions).

Additionally, there are two secret achievements:

Secret achievement (10 points): Unknown.
Secret achievement (10 points): Unknown.