Here is the full list of all 13 Backgammon Blitz trophies - there are 9 bronze, 3 silver and 1 gold.
Use every Power-Up at least once
Roll a double of each number
Use 3 different Power-Ups in a single game
Win 3 online games in a row
Win an online game against a player with a higher rank
Block all 6 of the home board points
Win by a Gammon
Win by a Backgammon
Play 5 local multiplayer games
Win a game on all 4 Backgammon sets
Re-Double the stakes of a game
Take an opponent's nip
Complete all tutorials