Lose Your Illusion hard mode is activated if engaging Thorium under three minutes. In this mode, Thorium will do more damage, and Sif will aid him with some new abilities (E.g. Blizzard).
Usually, the challenging part is to stay alive during adds phase, the balance between threat and speed to bring down the adds.
For me, the fight is pretty similar to normal mode, stay out of Blizzard, run away from Lightning Charge and keep a distance from others to avoid Chain Lightning.