Here is the full list of all 36 Battle vs. Chess (GFWL) achievements worth 1,000 gamerscore.
Win a Classic Game by Checkmate
Play a game to Stalemate (Classic Game)
Complete 5 Order missions
Complete 10 Order missions
Complete 15 Order missions
Complete 5 Chaos missions
Complete 10 Chaos missions
Complete 15 Chaos missions
Capture 100 pieces
Win a game while possessing 2 pieces less than your opponent (Classic Game)
Capture all enemy pieces and then checkmate the king (Classic Game)
Win online game against the player with a higher rating
Win a game in less than 5 minutes (Classic Game)
Win a game in less than 30 moves (Classic Game)
Promote your Pawns to every possible major piece
Place your opponent in Check by Castling (Classic Game)
Capture a Pawn 'En passant' (Classic Game)
Move your King to the opposite side of the board (Classic Game)
Place your opponent in Check 10 times in a single game (Classic Game)
Place your opponent in Check using 5 different pieces in a single game (Classic Game)
Win a single game in every game mode
Capture 5 pieces with the same piece during a single game (Classic Game)
Promote 3 Pawns in a single game (Classic Game)
Complete 20 levels of the 'Treasure Hunt' challenge
Complete all puzzles
Move an opponent into Checkmate using every piece
Play 100 games
Earn at least a Bronze Medal on every mission
Earn at least a Silver Medal on every mission
Win 20 games online
Play over 1000 turns
Earn a Gold Medal on every mission
Reach an online rating of 1200
Complete all challenges, puzzles and missions
Beat a Level 6 AI opponent in a Classic Game
Earn every achievement