If you are going to play story mode for your hardcore character, TCrash55's solution works great, however if you are looking to pick this up quickly, start a seasonal character in hardcore mode and jump into adventure mode. Gain a few levels until you have all your gear slots filled with a preference toward Life per Second gear, then jump over to Act IV and teleport to The Silver Spire Level 2 and kill Diablo. At level 20 with several pieces of Life per Second gear she was not able to drop my health below 90%. This method will also work for May His Death Satisfy You.
With this character you can also work on bounties for Batting 500 as well as working toward level 70 for Above and Beyond (Hardcore)