This will unlock on any difficulty, after you finish the story Mission 12. Completing all Gigolo missions, challenge missions, and side missions isn't required for this.
There is an additional achievement for finishing the game on Normal, Hard, or Very Hard (the latter of which is only unlocked after one of the other two). There is no additional achievement for finishing the game on Easy (this is pretty much it). This one stacks with the difficulty-based achievements (meaning you'll get both), but the difficulty-based achievements don't stack with each other (meaning three times through all missions to get all three).