Which day of Shavuos are you asking about? On the first day, those who daven “netz” generally do not have what I would call a “leibidik” davening. “Second minyanim” would be what you are looking for. Many of my friends stay up to learn but go home and sleep from around 4:30 AM – 8:30 AM and then daven.
As noted above, you are unlikely to find many “leibidik” shachris minyanim on Shavuos…most of the potential “celebrants” are barely awake and feel fortunate they can daven with a modicum of kavanah.
Many Yeshivos have “yeshiva” over Shavuos. I believe most Yeshivos would have dancing at night after Maariv and before the night meals (that’s what we have when I was in Yeshiva).