Now I have finally downed Mimiron, one of the keepers in Ulduar. It was at times a really intense, but fun, encounter to heal.
The first phase (Leviathan Mk II) is a walk in the park and what a holy priest needs to attend to, is to put Guardian Spirit on the tank just before Mimiron cast his Plasma Blast. I initially could not spot the warnings for that one, but Big Wigs warns you when the cooldown is off with "Plasma Blast soon!" (or something similar) followed by an emote "Casting Plasma Blast". From the emote you have about 3 seconds until it hits. Apart from that you basically put a heal on anyone being hit by Napalm Shell.
Phase two (VX-001) is the hard one for healers. The raid will continuously take a lot of damage. We put the range in two groups to avoid everyone being hit by Rapid Burst. I learned that casting Prayer of Healing when being hit by Rapid Burst, is not a good idea. All the interruption makes the casting time take to long (my spec do not contain Martyrdom which might help). We also tried to heal on "the other" group to get though our heals more efficiently. Also remember too keep an eye open for Rocket Strikes, if you get hit you're dead (talking from experience). [I need to check why we were standing in groups. I have probably missed something but from reading on Rapid Burst it might be more wise to spread out more?]
In Phase three (Aerial Command Unit) the healing get down to more normal levels. We had three tanks (one for the Aerial Command Unit, one for the adds, and we had one taking the Bomb Bots) to look out for and that worked fine (we had three healers by the way).
Fourth phase is a mix of the previous phases, but without some of the abilities. We had two tanks (and a third acting as assist target for the chest-part) so one healer was put primarily on raid healing. We lost a healer part of this fight which made it extra intense, but also very fun to play.