Here are some initial questions:
Did the achievement glitch on your account?
Did you start out on SuperSoldier Difficulty?
Did the Veteran 3/7 achievement unlock?
Did you access the tutorial from a new game or through the menu?
Prior to campaign completion, did you replay missions through mission select?
Yes, I did them in supersolider difficulty too.
If it didn't unlock initially, how did you finally get it to pop?
Did you press the X button to skip cutscenes either at the end of a chapter or during a mission briefing?
I skipped a lot and watched some, randomly.
A Clip Full of Hate