Ok, this doesn't appear to need to be consecutive days, as my profile said I'd only unlocked 1 of 10 on the website and I thought I'd start logging in on the Xbox app to stack with the 20 day consecutive achievement.
However, when I opened the app for the first time in over a year on the Xbox, this popped for me, so guessing that you can get it for logging in on 10 different days, not necessarily consecutive ones.
Hope that helps.