All of the "Calorie Score" achievements are cumulative and count across any type of game mode or session that you play. There is a Calorie meter on the main menu of the game that will tell you how many you've burned to date and how much more you need for the next milestone. The average person will burn at best +/- 100 calories per 12 minute workout so if you just play the game, you are looking at over 20 hours of workout time before getting to 10,000. This does not include load screens and menu selections.
To get there faster, set your weight to 396 which is the maximum allowed in the game. Start up the "Fitness Classes" and select Cardio Boxing. Then choose the 12 minute gold or silver workout (you will have to unlock the entire class by playing the individual segments first) and pull over a chair at the beginning. You can use either a rocking chair or swivel chair. Simply sit there and start rocking or spinning and watch the calorie count soar. Adjust the position of your chair to maximize the calorie burn. Now you will be burning 400+ calories per 12 minute workout so your total workout time is greatly reduced to 5 hours. This method is extremely boring though, so I'd recommend doing it in chunks of 3 sessions per day. You'll be getting 1000+ calories per day and be done in 9 days.
Also, go ahead and do everything else in the game first before "simming" your way to 10,000. It will make the road that much shorter if you had already burned 1000 calories before starting the big push to 10k.