The best way to embarrass your teenage daughter will take some planning and possibly aerobic exercise.
The first step is to learn what music she listens to and memorize the lyrics, especially the refrain because those are the moments you'll want to sing loudest.
It's especially relevant to note that volume is of higher priority that being able to carry a tune or knowing every single word to the song. In fact, it might be best to intentionally make up some phrases that are close enough to the words to sound correct but are completely wrong. Or random insertions of "LA, La!" and clapping.
This should bring about an embarrassment level of a 6 out of 10. You know, for those times when you're driving your daughter and a group of her friends to a movie or soccer game or wherever. Whatever song comes on the radio you must be ready!
For true mastery, you'll need some space to execute specific dance moves that more or less (go for "less") ape the dance moves from the video as you sing loudly to a song that you only know 3/4 of lyrics to. This is where the aerobic exercise comes into play.
If you've ever wanted to see your daughter actually phase-shift to another dimension -- dimension 22 where there is no Time and only Embarrassment exists -- a properly executed (i.e. fumbled) dance routine in time to the latest Miley Cyrus tune (or whatever tunes your daughter enjoys) will allow that kind of inter-dimensional travel.