Did the achievement glitch on your account?
Did you start out on SuperSoldier Difficulty?
Did the Veteran 3/7 achievement unlock?
Yes, in conjunction with the 3/7 SS achievement.
Did you access the tutorial from a new game or through the menu?
Through New Game on SS.
Prior to campaign completion, did you replay missions through mission select?
Yes, many times to collect missing Blackboxes, Power Module requirements and miscellaneous achievements.
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?