<Axis> of Dark Iron's strategy for defeating Karathress is here:
http://www.worldofstrats.com/Karathress/tabid/66/Default.aspx
This thread is for discussion of the strat and any additional questions about how to defeat this boss!
A couple points that could be added to this fight, just from what I've seen to help out the shaman who'd be healing the priest boss.
-Until the raid moves to kill the priest you should be casting a down ranked Healing Wave (7 or 8 I'd say), the damage will spike a bit but its nothing too bad when the raid moves in your priority will shift from tank healing to raid healing (because by now other healers will shift to help you heal the tank) from that point on you'll mostly be chain healing.
-A major reason why a resto shaman is needed for this job is because of earth shock, the raid will need you to interupt her heals otherwise the fight becomes much much longer. A macro that can help you do this is:
/Stopcasting
/Target Fathom-Guard Caribdis
/Cast Earth Shock(rank 1)
/targetlasttarget
This will allow you to just mash earthshock the second you see her begin to heal.