Talents and Glyphs:
http://www.wowhead.com/talent#bfMoZMZGbGdMzrd0fo:sRMqVM0zV

The main difference between normal and heroic mode from a shadow priest soloing perspective is that the boss will now cast Firestorm instead of clawing across the middle. Aside from that the boss also has a massive 65.7 million health pool, a massive 70% increase from normal mode, and yet the player still only get until the third tornado phase to bring it all down. This makes the fight an insane DPS check.

To achieve the DPS required, ilvl must be high (at least 403+) and a lot of mastery stacking is required. Not only that, it is also of vital importance to reach 25 stacks of the haste buff as early as possible. The trick is of course to double-dip on the rings, ie, get 2 stacks out of 1 ring, which I will explain below.

When the air phase starts on heroic mode, the boss will move either clockwise or anti-clockwise. The boss will always spawn a set of 2 rings in the same position before randomly changing to a new position (or remaining in the same position), with the first set of 2 rings always being on the boss's right. Using this to our advantage, it is advised to simply fly through the first ring of each set to determine its location, before preemptively fly to the location of the second ring and wait for the ring to spawn. Do not fly again until the second ring has despawned. This means that as the second ring spawns, the player will gain a stack, and as it despawns, the player will gain another stack. After this the first ring of the next set will spawn and thus the player should simply repeat the process. It is advisable to get at least 20 stacks before the first Firestorm in order to not fall behind on DPS.

Each air phase will have 2 Firestorms. Since there isn't enough stacks of the haste buff when the first Firestorm hits, it is advised to Dispersion through the last few ticks. However for the second Firestorm, the DPS will be high enough so that Vampiric Embrace will be high enough to keep alive. If not, simply cast a Power Word: Shield like I did.

The strategy to deal with the tornado phase as well as the burnout phase is pretty much the same as normal mode, except I saved Dispersion during the time when the boss reaches 100 power. Specifically I used Dispersion when the boss is at 93 power, and proceeded to tank the boss until she flies back up again. This prevents me from being knocked too far back, and lose out on DPS time. Also during the tornado phase in heroic mode, it is advised to refresh dots and throwing a Mind Flay or Mind Blast even during Harsh Winds. However don't do this when Harsh Winds goes beyond 3 stacks. Because dots are refreshed during Harsh Winds, it is very likely that these dots are still ticking as the boss falls to the ground for the burnout phase. This can cause some problems for players with the Cunning of the Cruel trinket as any procs that happen during the burnout phase will damage nearby adds and cause them to aggro. To solve this issue, I switched out my Cunning of the Cruel trinket for Necromantic Focus.

That's pretty much all the changes that I made for the heroic mode of the Alysrazor encounter. Keep in mind that although the boss's health is increased by a massive 70% on heroic mode, the length of the fight on heroic is actually 2 or 3 minutes longer as well.