To unlock Über Hardcore mode, you need to clear every level on Hardcore mode.
To unlock Hardcore mode, you need to clear each of 4 boss levels with at least 4 Stars while playing on the Hard difficulty setting.
On Hardcore mode you have only one life and no checkpoints. You must get through the whole level in one attempt.
General tips:- Always take available Health Pickups.
- Since you only have one life, take your time when playing through the level.
Either way, i have cleared
Über-Hardcore aswell and put my run down below, to show you how every level is done without dying.
Good luck