Here is the full list of all 13 Backgammon Blitz achievements.
Complete all tutorials
Win by a Gammon
Win by a Backgammon
Roll a double of each number
Re-Double the stakes of a game
Take an opponent's nip
Block all 6 of the home board points
Play 5 local multiplayer games
Win an online game against a player with a higher rank
Use 3 different Power-Ups in a single game
Use every Power-Up at least once
Win 3 online games in a row
Win a game on all 4 Backgammon sets