There does not appear to be any kind of tracker for this. When I finished the game I played Spiral Cliff one time and got this. I used Spiral Cliff because there's a lot of enemies in a short time, and at the end a ton spawn. You can also free the soldiers to be a meatwall for you, though I don't think you get experience for their kills, so their kills might not count toward 10,000. Either way you should not have to play much after finishing the game to get this.