Here is the full list of all 15 Stress Chess achievements.
Win Your First Game
Save All Three Kids Without Any Undos
Complete A Level With Only Mc'Chess Kid Left
Complete Campaign 1
Complete Campaign 2
Complete Campaign 3
Complete Campaign 4
Complete Campaign 5
Complete Campaign 6
Complete Campaign 7
Complete Campaign 8
Complete Campaign 9
Complete Campaign 10
Complete Campaign 11
Complete Campaign 12