Got back to playing this game after seeing the barrage of BanG Dream! Posters in Akihabara. It was on the trains, the stations, the billboards, the streetlights... They really have a way of pulling you in, huh?
Max out all of your one and two star characters and watch their stories. (Band > Members > Characters > watch the stories on the bottom) You get 75 stars in total for watching one character's stories. You can get 7k+ stars by just watching your 90+ one and two star characters. Don't watch the second story of three and four star characters unless you got a LOT of large shards.
Be in the top 1000 in events. Everyone that is in this range will get 500 stars after the event ends. I recommend having at least 100% event bonus (make your band become the featured type and have featured characters if possible) and playing multiplayer (you get around 50-60% increase in points) at 3X Live Boost to save time and get more rewards faster. Also set your area items so that it will help increase your band's power, this will help increase the amount of points you get. For Challenge Live Events, if you play 18+ games (3x Live Boost in multiplayer) and you use all of your CP, you can get in the top 1000. If you get around 3000+ points in one 3X multiplayer game, then there's a high change you'll be placed top 1000.
Master all the songs currently in the game, get ss and full combo. This will give you 22000 stars in total. (110 songs X 200 stars)