The augments you mentioned work, but do not appear in the passive skills window. This is a design issue that we have reported to the Dev team.

Here are the test results on naked character with Emperor's Special Cocktail:

+13 Bloody Krishna Fighter - Critical Damage = 41,807
+13 Bloody Krishna Fighter with 20% P. Critical Damage Augment - Critical Damage = 50,168
+13 Bloody Krishna Fighter with 20% P. Critical Damage Augment and Queen Ant's Soul Ring (15% P. Crit. Dmg) w- Critical Damage = 57,694

Here are the test results on your character with everything equipped with Emperor's Special Cocktail:

+13 Bloody Krishna Fighter + all of your jewels/talismans/shirt/cloak equipped - Critical Damage = 206,905
+13 Bloody Krishna Fighter with 20% P. Critical Damage Augment + all of your jewels/talismans/shirt/cloak equipped - Critical Damage = 248,286

The augment is working without issue. I had the random damage variance set to OFF, which players cannot do.