The Stonecore is a new dungeon in the World of Warcraft: Cataclysm expansion. It’s a cave style dungeon that’s targeted at level 82 to 84 on Regular mode, and restricted to level 85 on Heroic mode.
Most of the trash isn’t too tough, but they are in fairly large packs so use Crowd Control as needed.
The bosses are listed in order, so here we go:
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Corborus
Remove the Dampening Wave debuff as it will absorb healing (4k normal, 15k heroic).
Keep moving to avoid Crystal Barrage  (AoE DoT with a 5 yard range, so easy to avoid).
Keep moving during his digging phase as well, as you will receive splash damage if you’re close when he comes out.
Slabhide
As with most dragons, stay away from his front to avoid Sand Blast frontal cone AoE.
Keep moving to avoid Eruption, which is a short range targeted AoE, but leaves lava pools that should be avoided.
Watch for shadows on the ground during his flying phase, because stalagmites will fall from the ceiling for a fair amount of damage.
Ozruk
Tank should keep him in corridor to avoid knockback.
Stay away from his front to avoid Ground Slam (500k instant KO within 8 yards). Easiest to run through him when he starts casting it if you’re fighting from the front.
Melee should move away on Shatter (close rang AoE).
Caster DPS should watch out for Elementium Bulwark which will reflect spells back at them.
Melee will take extra damage during Elementium Spike Shield which is a thorns type spell.
High Priestess Azil
Adds come in several times during this fight, always from the right side (where you came in from).
She casts Gravity Wells on the ground which damage both friendlies and enemies, so drag adds through them whenever possible. One strategy is to start the group on the right and progress to the left since Gravity Wells will be targeted on players, and adds come in from the right, so they’ll always have to run through them to get to your group.
Keep an eye out for your healer, as any heals as the adds are coming in will likely make them run straight for him or her. The adds don’t have much health, but as a mob they can take down healers fairly quickly.
Try to interrupt her Force Grip if possible, though it’s a fairly fast cast so it may be tough.
Melee should move away from her when she casts Energy Shield (close range AoE, and 75% damage reduction) and keep moving as she’ll be hurling rocks at players for a short time.