Nightmare difficulty is unlocked after completing the game once. In Nightmare difficulty, when you die, you have to restart the ENTIRE GAME.
Put your first 3 points into Teleport Slash for its healing abilities, then max out the other skills that feed into Teleport Slash.
Part 09 - Judicator's Tomb
Part 10 - Psychameron & Achidna
Part 11 - Sentinel's Gaze, Boneriven & City of the Dead
Part 12 - Lair of the Deposed King
Part 13 - The Scar/DIED DURING PLATFORMING & GUIDE HIATUS
Spoilers: Double rolling is about 30% faster than running