Video is a bit choppy at the end. Apparently my computer decided to give me some FPS lag at the end as a last ditch effort to get me to wipe.
From a soloing perspective, the main difference between the normal and the heroic mode of Lady Deathwhisper is that the adds from phase 1 continues to spawn during phase 2. Add waves now come every 40 seconds (instead of 1 minute on normal) although the abilities of these adds remain the same. Aside from hitting a lot harder, the boss health is now doubled compared to normal mode. This makes the encounter a bit of a DPS race.
With that in mind, the primary objective of phase 1 is to push the boss into phase 2 as soon as possible, preferably after 4 add waves. If a fifth add wave spawns, it is most likely a wipe to the enrage timer, although victory may still be possible for a priest in full heroic 4.3 gear. The strategy used in phase 1 in heroic mode is still the same as normal mode, with the exception that there is now less time to DPS boss since add waves come more often. The kill priority for the adds are also the same, with Adherents being the highest priority. A wipe is imminent if an Adherent:
1. Becomes reanimated
2. Gains a buff that reflects all magic attacks
3. Casted Curse of Torpor so many times that it no longer becomes possible to beat the overall enrage timer.
Once the Adherents are down, focus on the Fanatics, and dispel their Vampiric Might if necessary. Aim to push the boss into phase 2 after 4 waves of adds for the best chance to survive the enrage timer.
Extra awareness is required for phase 2 as the adds continue to spawn. Their spawn rate is the same as phase 1, but luckily they now only spawn 1 at a time, and the exact add is chosen at random. The best way to deal with the adds is to keep health topped up just before they spawn, and nuke them down as soon as they appear. The worst case scenario in this situation is to get affected by another Curse of Torpor. When this happens, cast every heal spell available except Flash Heal and use Dispersion to mitigate incoming damage. Using Shadowfiend to get aggro on the boss whilst dealing with the adds is also a nice strategy, however keep in mind that the enrage timer is tight, so it might also be worthwhile to just use Shadowfiend when there is no add around in order to land some DPS on the boss.