Here is the full list of all 11 Lynium achievements.
Play 50 times
Pass a beatmap with difficulty 4 or more
Pass a beatmap with difficulty 5 or more. You are playing very good
Pass a beatmap with difficulty 6 or more. Who are you?
Pass a beatmap with difficulty 7 or more. OMG
Pass a beatmap with 100% Accuracy
Get the #1 World Ranking in one beatmap
Pass a beatmap with difficulty 2 or more
Pass a beatmap with difficulty 3 or more
Pass a beatmap
Pass a beatmap with difficulty 1 or more