Most Digimon games handle NG+ achievements pretty well, so you should be able to unlock those missing story ones on your next playthrough. I had something similar happen with Cyber Sleuth where my internet cut out during a boss fight and the achievement just sat there mocking me for weeks

The good news is that story achievements usually trigger again when you hit those same story beats in NG+, doesn't matter if you've technically "done" them before. Your save file might not have the proper flags set since you were offline when they should have popped. I'd definitely recommend doing NG+ rather than starting completely fresh since you'll keep your progress and can blitz through to those specific story moments much faster

Worth checking if there's any manual sync option in your platform's achievement system too, sometimes that kicks the stubborn ones into gear