The only difference between normal and heroic versions of this boss is that his melee attacks are 50% stronger on heroic, and he will cast Bonespike Graveyard during Bone Storm. Since Bonespike Graveyard does nothing when soloing/tanking the boss, therefore from a priest soloing perspective, nothing has changed about this fight aside from the extra health and damage.
Normal mode Marrowgar can be tanked and barely outhealed with Flash Heal spamming (depends on ilvl and spec) but since heroic version hits 50% harder, tanking it head on is no longer a viable option. Instead, a kiting strategy is recommended, as much as I hate kiting (makes me look away from the boss... and hence the boss isn't present within most of the footage, makes the video kinda..meh).
Kite the boss around the perimeter of the room, and each time he catches up, pop a defensive CD, such as Dispersion or Desperate Prayer. It is recommended to glyph Dispersion for this fight for the shorter cooldown duration (you will need it). The only way to gain distance between you and the boss is when the boss stops to cast Bonespike Graveyard. After casting this 3 times, he will then proceed to cast Bone Storm. Unleash every bit of DPS you can during this phase. Don't worry about Cold Flame, they do nothing. However it is recommended to begin kiting again just after the boss finishes casting his second Bonespike Graveyard during the Bone Storm, so that as soon as the boss finishes Bone Storm, there will be maximum distance between you and the boss, giving you a headstart to the kiting process.
The entire kiting process may take a few attempts to nail down, but once you nail it down, it should be all smooth sailing from there. Watch out for the Dazed effect when the boss does land some inevitable hits on you, some badly timed Dazes can spell a wipe.
The fight can be done with the usual shadow raid spec, but it is preferable to spec into Holy to pick up Desperate Prayer for the extra cooldown. As for glyphs, Dispersion is pretty much required.