This DOES NOT stack with "Ten Large!" That means that you must get 10,000 moves where you do well enough to get a nice rating (circle turns green), but not well enough to get a flawless rating. As you play through the game, you will likely find a number of songs where you get a large number of nice moves, like Stronger or The Breaks from DC2. You can try playing these songs frequently, or you can play songs where you try to just muddle through. Some songs will give you a nice rating if you play on easy but only do hand motions without moving your feet. You will be making progress with this after every song, barring an amazing performance, so there really isn't much need to grind from this until after you have passed the 10,000 Flawless moves.
There is no way of seeing how many moves you have gotten flawless or nice on, unfortunately. However, if you sit in the main menu it will give you random stats. One of those stats is "Songs played," which will allow you to get an idea of how close you are if you have a vague idea of how many flawless/nice moves you are getting per song.