Halacha vs. Minhag

Harav Hagaon R.Y.S. Eliyashiv zt”l said, Those who go to sleep before עלות השחר not having davened Shachris should make sure to do so, at least a half an hour  before עלות השחר otherwise, it would have been better had he not stayed up for the night altogether. Staying up the night of Shavuos is only a Minhag Not going to sleep before עלות is a Halacha.