You must visit Calendar Man on:
New Year's Day
Valentine's Day
St. Patrick's Day
April Fool's
Mother's Day
Father's Day
Independence Day
Feast Day of St. Roch (It's August, they had to dig deep for this one)
Labor Day
Halloween
Thanksgiving
Christmas
You can use Google to find out what exact day these holidays correspond to in a given year (obviously some like New Year's and Valentine's are the same every year, but others like Mother's Day and Father's day change year-to-year). These are real world dates, not in-game. Play offline and change your system clock to the specific days if you don't want to waste a whole year on this. If you want your achievement to be timestamped and not marked as offline, pick whichever holiday on this list will happen next, change your system clock to check off every other date while offline, and then wait for that next holiday to come up in real life and talk to Calendar Man while online.