Here is the full list of all 36 Battle vs. Chess (GFWL) achievements worth 1,000 gamerscore.
Get all achievements
Achieve online rating 1200
Win 20 games online
Play 100 games
Win a game, having 2 pieces less than the opponent
Get stalemated
Capture all enemy pieces and then checkmate the king
Move a King to the opposite side of the board
Make a check by Castling
Make check by 5 different pieces in one game
Promote 3 pawns in one game
Promote a pawn into all major pieces
Capture a pawn 'En passant'
Win online game against the player with a higher rating
Win a game in less that 5 minutes
Win a game in less that 30 moves
Win an AI opponent with the difficulty of 6 in a classic chess match
Capture 5 pieces with one piece in one game
Make check 10 times in one game
Win one game in each of the game modes
Win a classic chess game by checkmate
Complete all challenges, puzzles and missions
Complete all puzzles
Complete 20 levels of the Mana Gathering challenge
Complete 15 chaos mission
Make checkmate by all pieces
Get bronze medal in all missions
Get silver medal in all missions
Take gold in all missions
Complete 10 chaos mission
Complete 5 chaos mission
Complete 15 order mission
Complete 10 order mission
Make 1000 turns
Capture 100 pieces
Complete 5 order mission