Part 1 (Azjol-Nerub, Culling of Stratholme, Halls of Lightning, Drak'Tharon Keep):
http://warcraftmovies.com/movieview.php?id=129751

Part 3 (The Nexus, Utgarde Pinnacle):
http://warcraftmovies.com/movieview.php?id=129773

Part 4 (Gundrak, The Oculus, Utgarde Keep):
http://warcraftmovies.com/movieview.php?id=130649

In my opinion the YouTube HQ Stream is the best quality of the streams offered.

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A protection spec Paladin solos various Wrath of the Lich King heroic dungeons in patch 3.2 on the Staghelm US server. Included in Part 2 are Halls of Stone and Old Kingdom.

Tracks:
Alex Gold - Stranded in Paradise (Agnelli & Nelson Remix)
Breakfast - Remember

If you liked this check out my other stuff:

Classic Hard Modes:
http://www.warcraftmovies.com/movieview.php?id=126783

Green Dragons:
http://www.warcraftmovies.com/movieview.php?id=123001

Blackwing Lair 6/8:
http://www.warcraftmovies.com/movieview.php?id=111227

Molten Core:
http://www.warcraftmovies.com/movieview.php?id=109587

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Responses to some comments:
About Sacred Shield and nerfing us, ya. As of the current PTR we can't Lay on Hands ourselves and Sacred Shield is virtually useless unless you're Holy, so if they go to live at all similarly our soloing ability will be hurt a lot for the harder stuff.

These runs tend to take about an hour without wipes, or two or more with the harder bosses. Going straight to Skadi and just doing him probably takes half an hour if anyone was wondering.

For the harder challenges like Gatewatcher, Sjonnir, Tribunal, and Anomalus I do reglyph and respec to optimize myself. This includes Glyph of Holy Wrath, Judgement, and Salvation depending on the situation and going into a more solo-oriented spec by dropping select raid talents. I also habitually alternate between a tank weapon with Seal of Corruption (offensive mode) and a healer weapon with Seal of Light (survival mode).

Addons that you can see here:
AF Tooltip Extreme
Bartender4
Deadly Boss Mods
eCastingBar
Elkano's Buff Bars
MikScrollingBattleText
OmniCC
Pitbull4
SexyMap
TidyPlates / CleanPlates / ThreatPlates
Titan