EDIT: Clarification about cold flame:
Cold Flame is constantly spawning under your feet. Even if you move, it will be under your feet again within the next second, forcing you to constantly move. For a melee class this is no problem. But for a caster class, this severely gimps DPS and healing.
For a priest:
Constantly moving = constantly no Flash Heals
Constantly no Flash Heals = WIPE from cleave
Therefore for a priest in this fight to survive, MUST STAND IN COLD FLAME.
Marrowgar was first solo'd by a DK back when it was current content. Hence this boss has somewhat became an iconic soloing target for many people.
This boss is quite simple in terms of mechanics and only has 4 abilities:
1. Cleave - the boss doesn't just cleave once every 4 or 5 hits, but pretty much 80% of the time. This cleave damage is intended to be shared between 2 tanks, but since this is about soloing, and the fact that priest has no proper pet as well as next to no kiting mechanics, this damage is unavoidable. Therefore this fight is extremely healing intensive.
2. Cold Flame - this is the fire that is spawned on the ground. Moving out of this is in fact NOT recommended as healing is already tight as it is without movement. Luckily the cold flame does very little damage and can sometimes miss or resisted.
3. Bonespike Graveyard - this ability impales a player on a spike but in solo situations, this ability does nothing. Hence whenever the boss uses this ability, it provides a small time gap to catch on healing.
4. Bone storm - This ability is similar to Alizabal's Bladestorm where the boss spins around like a maniac. The damage from this ability is intended to be an aoe, hence it does very little. Use this time to DPS boss or catch up on healing.
In addition this boss has a 10min enrage timer, so at least 11.7k DPS is required to beat it. Overall this fight requires a high gear level on the priest. There are times during the fight where the priest might be slightly ahead on the healing and can afford to spare a GCD to apply a dot on the boss and it is strongly recommended to do so in these situations.