The Master of the Sheerdrop Spire (Kilte Airāvata) appears to be just a fancy rock formation when you first enter its chamber. Once you grapple at its Master Flesh, however, it will wake up and begin moving around. He can't move very easily since he is heavy and made partly of rock, especially his lower half and arms. He will move by jumping and turning in the air to face you.
As with most Master fights, this fight relies on your Oraclos Chain skills more than your sword or other weapon skills. This Master is quite hard to beat, and you can quite easily use up half of your remaining curse time in the battle without realising it.
Its Master Flesh is on its back, and it insists on facing you most of the time. This is the difficult part. Getting behind it is hard. The best way I found was to grapple one of its legs to one of the rocks it makes when it does that spinning attack. However, I had plenty of difficulties with this, since when you do get behind you have to release the chain, after which you have a 5 second timeslot (max) in which to grapple his Master Flesh. It is also hard to get behind him altogether, since the chain doesn't last long at first and he may have escaped by the time you navigate around the same rocks you're grappling him to. Later on it gets even harder, as he will turn around the second the Chain releases his legs.
A quicker way to get behind the Master is to run very close to the master, always trying to run behind him, and dodge twice as he makes a downward stab and swipe. Sometimes you will have passed the rocks made. Other times you will be caught on them: Simply hit the rocks with your weapon and continue.
It is possible that a better way to get behind him would be to power up the chain by pulling it away from is legs before grappling it to the rock, for this would allow you more time to get behind him. I'm not sure if this will work, however.
Another safer however, longer way to get behind the master is to repeatively pull on the masters legs which after numerous pulls will cause him to become paralized which gives ample time to get behind him for a full pull, however this can take minutes and use up huge amounts of time and swinging the wii remote can get excausting however none of his attacks will ever reach you.
The quickest method is to allow the master to build the rocks, (do not destroy them) and chain his leg to one of the rocks. Then, run behind the master and take the chain back. After you take the chain back, grapple his weak spot. This usually gives enough time to get a full chain bar, thus, you are able to finish him off in ample time. However you must repeat the first step in order to keep dealing large amounts of damage.
(I found that when you get behind him, it is actually relatively easy to stay behind, as he just looks around and does little hops occasionally, making it easy to get a full chain pull. It's only if you pull or take too long that he'll do a big jump and fully turn towards you.)
He basically has three attacks. The first and most common is when it hits the ground with its fist and summons boulders to affect your movement through the field.
Another one of its attacks is where it spins around, creating rocks that fall around it. There is no real trick to avoiding this, just stand back a bit. It shouldn't bother anyone too much.
And finally, when its life is getting low he crashes his fist to the ground and starts growing vines towards you to hit you. It's easily avoided by dodging. You don't even have to take the chain back.