Here is the full list of all 20 Radium achievements.
Fail at a level
Get three points on any level.
Get three points on level 8.
Get three points on level 16.
Get three points on level 24
Get three points on level 32.
Get three points on level 40.
Get three points on level 48.
Get three points on level 56.
Get three points on level 64.
Get three points on level 72.
Get three points on level 80.
Get three points on level 88.
Get three points on level 96.
Get three points on level 104.
Get three points on level 112.
Get three points on level 120.
Get three points on level 128.
Fail fifty times.
Fail hundred times.