Here is the full list of all 35 3in1 Game Collection: Backgammon + Checkers + Mills trophies - there are 20 bronze, 12 silver and 3 gold.
Win the first game of Backgammon
Win 10 games of Backgammon
Win 20 games of Backgammon
Hit 2 blots within one turn
Hit 4 blots within one turn
[Backgammon] Achieve a score of more than 20 Points
Prevent your opponent from re-entering
Throw a Double
Throw a double with sixes
Win the game before your opponent bears off their first piece
Block your opponent's first quadrant while they have at least one blot on the bar
Win 10 games of Checkers
Win 20 games of Checkers
[Checkers] Draw against your opponent
[Checkers] Capture 3 pieces during one turn
[Checkers] Capture 5 pieces during one turn
[Checkers] Capture a total of 100 pieces
Capture a King
Possess a king
Possess three kings
[Checkers] Win a game by blocking your opponent
[Checkers] Win while playing with white pieces
[Checkers] Win while playing with black pieces
Win the first game of Mills
Win 10 games of Mills
Win 20 games of Mills
[Mills] Win a game by blocking your opponent
Possess 2 closed Mills
Possess 3 closed Mills
Move one man out of a Mill to create a new Mill
Create a Mill with only 3 remaining pieces
[Mills] Win with white pieces
[Mills] Win with black pieces
[Mills] Win a game with 5 pieces max
[Mills] Win with 3 remaining pieces