Here is the full list of all 16 Chess Brain: Dark Troops achievements worth 1,000 gamerscore.
All levels completed
Level 30 completed
Level 28 completed
Level 26 completed
Level 24 completed
Level 23 completed
Level 20 completed
Level 17 completed
Level 16 completed
Level 13 completed
Level 11 completed
Level 10 completed
Level 8 completed
Level 6 completed
Level 4 completed
Level 1 completed