Lips

There are four kinds of cups, and bronze is the lowest level. You get them by placing in the top xxx of the world leaderboard on a song, bronze being 1000, silver 500, gold 100. I'm not sure if platinum is top 10 or top 1 because I've never placed higher than 11th on a leaderboard.

You can only earn one cup per song, though you can upgrade it over time by getting a higher level. That's still only 1 though, so you'll need to do this for 20 different songs.

You'll know you're earning a cup because a cup will appear on your screen while you're singing if your score is high enough. Next to it is a ranking that will go down as you pass more people on the leaderboards. You won't actually earn the cup until the score screen, though.

At this point a lot of the leaderboards are saturated so I'm writing this to help you maximize your chances. You can do so in one of two ways:

1) Buy and sing DLC. The less popular a song the better, but of course this costs money. It will be harder to earn a bronze cup in some of the most popular songs on DLC than with the least popular on-disc games. Your chances go up the more recently a DLC song was released, obviously.

2) Sing co-op/duet (not versus). You'll be compared against a different leaderboard and not nearly as many people play this mode. In this mode all the points from both singers is pooled into a single high score. With some songs, you might even have a bronze cup at the very beginning.

Obviously your best chance is to sing co-op/duet in a DLC song.

It's best to get this out of the way sooner rather than later, because this will only get harder to get as time goes by, unless they reset the leaderboards for some reason.

I would say do this in Duet (Co-Op) Mode
I'm working on a list of easier songs to get the 20 bronze cups in:
So far:(All 80's Disk)
1. Our House - Madness
2. Whip It - Devo
3. Walking On Sunshine - Katrina & The Waves
4. Super Freak - Rick James
5. Centerfold - J. Geils Band
6. Micky - Toni Basil
7. Love is a Battlefield - Pat Benatar
8. Bad Reputation - Joan Jett And The Blackhearts
9. Boys Don't Cry - The Cure
10. Cruel Summer - Bananarama
11. Rio - Duran Duran
12. Blue Monday 88' - New Order
13. The Look Of Live - ABC
14. Let's Dance - David Bowie
15. To Shy - Kajagoogoo

This also takes some singing ability.