People have been unsure how to unlock this achievement, no it's not glitched but either by design or by mistake they want you to do it all again. In a strange way the achievements do not stack, for example if you beat Contra Arcade, you get the achievement for it but you do not unlock the progression of it being beaten for True Contra Warrior.

I'm not sure if you can simply beat it twice for each or if you have to beat all games then go back and beat them all again.

My recommendation as I know this works for sure and will save you time, approach the end of each game, right before you finish that last boss make a save state. Do this for all games, then after all the other achievements are unlocked load up each game one at a time and load your ending, the progression unlocks the same time your other achievements did, at the start of the credits. Do this for all games and your final achievement will unlock. Please note for Contra Hard Corps which has multiple achievements for different playthroughs that you still need to load an additional ending after you collected all those achievements. Additionally you do not need to beat Contra 3 or Probotector Alien Rebels on hard like someone has suggested on other boards.

Happy Hunting!