The hard mode of the Mimiron encounter is initiated by pressing the red switch at the back of the room. Doing so will activate the self destruction sequence with a countdown timer of 10 minutes. This means that Mimiron must be defeated within 10 minutes, which is 5 minutes shorter than the time limit on normal mode.
Aside from the 25% increased damage dealt by everything involved in the encounter, the major noticeable difference on hard mode is the presence of fire on the ground. For a geared level 85, this fire damage is rather trivial, but for the level which this encounter is designed for (level 80), this fire is rather deadly. What's worse is that the fire spreads towards the nearest player and does not despawn. The only way for the fire to despawn is when the boss uses a frost bomb, or from emergency fire bots which puts out fires but can also knock players back with their jets of water.
From a priest point of view, the fire does not really add new challenge to the fight. It's the increased damage and health of the boss and the adds that requires a more coordinated usage of cooldowns. The first 2 phases are dealt with using the same strategy as normal, with most likely an extra plasma blast being casted in phase 1. In phase 3, it is necessary to use a Magnetic Core (dropped from Assault Bots) on the boss to allow a quicker burn. This wasn't necessary on normal mode though it can speed things up. As usual, kill the bomb bots if GCDs can be spared. However it is preferable to ignore some of the bomb bots so that the boss can go down quickly. Keep in mind that the damage a Junk Bot can deal before it dies is most likely greater than that of a bomb bot so it is preferable to take damage from a bomb bot rather than having to deal with an extra junk bot because the boss didn't go down fast enough.
The strategy for phase 4 is still the same as normal mode, although now it is much harder to survive. Do whatever possible to keep alive but at the same time do whatever possible to gain extra mana, as well as do whatever possible to gain distance. On top of everything, make sure to avoid all the special lethal attacks from the boss as well as any emergency fire bots and frost bombs. Just like normal mode, all three parts must go down at roughly the same time.