First, Val'kyr Heroic:
The main difference with normal mode is that they hit really hard (I used a stamina trinket and a stamina flask). And that their heal shall not pass. Or the berserk timer will. I believe that the shield ignores light/dark essence, but either way putting up hunters mark + serpent sting + FD if your aggro is too high makes you lose time, so try to dps the val'kyr that will bubble next. Use rapid fire if you must switch to dps a shield. Oh, and a new dot, touch of light/darkness appears, but can be dispelled by switching essence.
Phase 2: run on the opposite side of the room, spawning patches but making sure Anub doesn't break them. At the last moment, FD. His spikes will go on your pet. Put your pet at about 30 yards then, once scarabs are too close to your pet, get up, hide behind an ice patch, and kill the scarabs on your pet. Anub should rush you, and you will need to start kiting him from one side to another. You can manage to break only 2 patches, 3 is the maximum (unless he bugs like in my video, but it happened twice in 40 phases 2).
Phase 3 is the most difficult. Leeching swarm will put you between 4K and 20K, and his dot hits hard.
Put up widow venom at the start, but it's useless afterwards.
-use a prismatic elixir.
-rotate healing/absorbs. I used ignored intervene on the first (make sure you use it asap, because anub likes to freeze your pet when you're at 4K), double chimera + engineering shield on the second, intervene on the third and health potion + intervene on the fourth.