This will not be a comprehensive boss guide, instead this will be a quick run down on things that you, as a resto shaman, should be aware of or tips to help make your healing of the encounter easier.
The giant stone turtle is probably one of my least favorite fights as a shaman healer. Not because it's a badly designed fight, on the contrary it's actually really interestingly designed encounter. No, it's because it is the one fight in the entire raid zone that really doesn't play well to shaman healing strengths. It's a great challenge, and a great way to push yourself to really explore your toolkit. The first thing you will notice is that this rather large fellow is lodged into the only way to progress further. The second thing you will notice is that Tortos has a penchant for throwing it's young Whirl Turtle babies at you at rather high velocity. If you get hit by them, you get launched in the air, you will count as moving and so will only be able to use instant cast spells like Riptide, Unleash Elements or making use of Ancestral Swiftness to snap off a quick heal or Spiritwalker's Grace to heal normally while in the air. I would recommend trying to keep your cooldowns handy for something else during the encounter. The trick with the turtles is that they are avoidable, and can be slowed down. You can help with this, and you should, by using Earthbind Totem. Helping out with this will help you avoid them, and the subsequent airtime, and that is something you really want to do.
The big mechanics of this fight that you really need to worry about are Quake Stomp and Rockfall. Rockfall periodically happens throughout the fight, where a stalactite will fall to the ground in an area highlighted by a blue circle, and nature damage based on the distance you are standing from the impact zone. The closer you are, the more damage you take. This is important to note because after a Quake Stomp not only will the raid suffer 30% of their total health in damage, but our shelled friend will increase the rate at which stalactites drop. This is where I suggest you use your cooldowns, such as SWG so you can heal on the move while avoiding those falling deathsicles. Healing Tide Totem and Ascendance are also very good here. Make sure that if your HTT is on cooldown that you have Healing Stream Totem. This is the big damage phase for the fight, so it's a matter of spacing out your cooldowns for each stomp phase.
The real downside of this fight is that there is a ton of movement, and people are constantly spread out. I highly recommend using Glyph of Chaining for this fight as it is immensely useful. I would also recommend looking at either Astral Shift of Nature's Guardian in place of the much beloved Stone Bulwark Totem simply because you'll likely be keeping down Earthbind constantly. It's a challenge for sure, as you're going to have to watch so many things to make sure you can heal when you need to and you will have to make use of your whole toolkit, but when the turtle is shattered it can be a very rewarding experience.
This boss is a little more friendly for shaman, there is a lot of grouping up, and quite a bit of raid-wide damage to contend with. It basically falls right into our comfort zone, and after a boss fight like captain McTurtle-pants it is very welcome. There are three different heads that you will be contending with for the fight, Flaming, Frozen and Venomous. Each head has a distinct ability that you will need to pay attention to. The Flaming head will cast Cinders on a target in the raid, it is a DoT that will deal fire damage every second for 30 seconds. Once dispelled, or if the timer for the debuff reaches zero, it will leave behind a pool of fire that will damage anyone that walks through it. You can dispell it with Cleanse Spirit, just make sure that the person is away from the raid group when you dispell it. The frozen head will use Torrent of Ice which again will target a random target in the raid group and will leave a trail of Icy Ground behind. Patches of icy ground can be cleared by people who have cinders running through them. The last specific ability to watch out for is the Acid Rain from the venomous head. It's a raid wide explosion that the further you are away from the epicenter the less damage you take. Despite these abilities, damage is pretty manageable.
Each time a head dies, though, is when the fun really starts. Not only will Hydra Frenzy kick in increasing the attack speed of the heads off in the distance, but each time a head dies, the Rampage phase begins. For 20 seconds our little hydra friend will deal massive damage to everyone in the raid. For each head that dies, this increases by 15%, so by the end you can guess that the damage will be quite high. The good news is that most strategies call for grouping up, take full advantage of this by utilizing your Healing Rain and your Chain Heal. Keep RT up on as many targets as you can, and don't forget about UE. I personally really enjoy Echo of the Elements on this fight as well, and I recommend giving it a try here. Use HTT on any rampage as long as you work it out with your heal team, but I recommend combining Spirit Link Totem and Ascendance and saving the combo for a later rampage. It's a fairly straight forward fight that you should be able to have a lot of fun healing through.
Totem Talk: Restoration lends you advice on healing groups, DK tanks and heroics and mana concerns in today's endgame -- or take a break and look back at the rise of the resto shaman. Happy healing, and may your mana be plentiful!