Do all Pirate's Booty missions need to be completed in the same mode in Borderlands 2 for Completionist?

I completed all missions in the Pirate's Booty DLC except for defeating Hyperius and Master Gee on True Vault Hunter Mode and then switched to Normal Mode to defeat the two of them. Completionist did not unlock. Does this mean that I need to go back and complete all of the side missions on Normal Mode in order to get the achievement?

Simply: Yes.

The all of the "Complete all of one DLC" achievements are for completing all of the missions in one game (thought it isn't that specific in the description). It treats the different difficulty modes as different saves, so the achievement wont be achieved through a combination of saves.

On the bright side, when going back to normal mode after true/ultimate vault hunter mode, you are incredibly powerful and can rush through the missions relatively quickly for the achievement.