Halls of Origination fluctuates between the shortest and longest heroic instance because, despite being seven bosses deep, four of those are optional, the three you have to kill are fairly basic tank and spanks, and the amount of trash is low. A two level instance, I'm going to break this down floor by floor.
Upon entering the Instance, the first boss you will come across will be Temple Guardian Anhuur. This is a pretty basic fight - the primary ability to worry about for the party will be Searing Light, a laser beam down from the ceiling leaving a patch of holy fire on the floor you should avoid - with the only real complication coming during a phase in which he will shield and become impervious to all damage until you flip two switches in the literal viper pit below him. You need to drop this shield so you can interrupt Reverberating Hymn, a channeled spell that will slowly build up a stacking holy damage DoT that will overwhelm the healer if allowed to run indefinitely.
On normal flipping these switches is instant but on heroic they have a 10 second cast time which is interrupted by any bite from the vipers. This means you can no longer just send a couple people down to tap the switches and run back up. Instead, you'll likely (at this point), need to move as a group from one switch to the the other assigning one person to flip the switch while the remaining DPS and Tank manage the Pit Vipers. It's a good idea for the person flipping the switch to communicate to the others to begin moving to the next when there's only 1 or 2 seconds left on the cast timer so everyone's moving instead of following you as you take off for the next switch and picking up vipers by being in front that will need to be pulled off so you can start flipping the next.
Soon as the shield's down, someone needs to interrupt the cast and you can either have someone take off to do so while you're flipping the second switch or have a class with a speed boost take off to do so when it's down, your call. Repeat this twice and you'll be moving on.
Take the left passage in the elevator chamber and you'll come to Anraphet. His chamber is full of non-elite respawning Trogg packs that can be AoE'd down and 4 mini elemental bosses that must be killed to release him. Their mechanics can be summarized pretty shortly:
Flame Warden: Casts an AoE called Raging Inferno below himself. Melee should run out when they see him start casting to avoid it entirely because it does significant AoE damage and, more importantly, stacks a fire damage buff on anyone it hits which doesn't play nice with the Lava Eruption's he'll be casting on random party members. You'll blow up real good if you mix those.
Air Warden: Casts Cyclones that chase random targets. Avoid.
Earth Warden: Casts Rockwave at random targets. If he turns to face you, time to practice your "waggle" skills and respond accordingly.
Water Warden: Bubbles random people, including the Tank, preventing them from taking any actions: break them out quick because there's no cap on his ability to do this and you'll quickly find yourself without anyone free if you don't. Also, water void zones, avoid.
Once you defeat these four, Anraphet will enter the room and execute a room wide AoE to obliterate the Trogg packs permanently so make sure everyone's at at least half health to be safe. His fight is pretty straight forward and consists of basically two phases, dodge the void zone and stress test the Healer.
Shortly after pulling, he'll start casting Alpha Beams four consecutive times at four random targets. This doesn't seem to hit the same target twice consecutively IME but it can target the same person again within the span of the sequence. This will leave a void zone where the person was standing that's persistent on heroic and should be gotten out of ASAP. Note: with each cast of this the prior set(s) tend to go a lighter shade of purple - they still hurt. The Tank needs to keep track of these void zones and move the boss so that melee continues to have room to work.
A few seconds after the Alpha Beam phase he'll break into Omega Stance and start channelling AoE damage across the entire room. This is a good time to pop defensive cooldowns to help your Healer though the phase. When this phase is over, a few seconds will pass and then the Alpha Beam phase will start the cycle all over again.
There is a soft enrage on this fight - the boss is stacking a health pool debuff on the party as the battle goes on so eventually he's just going to start squashing people - but you should be able to avoid it with good DPS.
Taking the teleporter behind Anraphet will return you to the elevator room and you've now the option to take the elevator up or go down the right tunnel to Earthrager Ptah where you've the option to fight on Camel Back. This absorbs some attacks and lets Caster classes cast while moving as if they were on a Siege Vehicle from the BG's - handy for Healers - but causes problems for pet classes or those that rely on pets as cooldowns: you'll have to forsake your pet for the Camel.
With an above and below ground phase, his core mechanics in the first are pretty simple. He'll cast Earth Spike on random players; watch for shifting earth below your feet and move to avoid or, at best, you're losing your Camel. Secondly, he'll occasionally "Turtle" and execute a fire AoE that can be safely healed through.
At 50% he'll dive below ground and spawn multiple scarabs and two Dustbane Horrors. The tank will want to pick these mobs up and everyone can just AoE them down while dodging Quicksand, a void zone on the ground with a "dusty" effect indicating its location. Once you kill these, he'll emerge and you'll finish him off as per the first ground phase.
Here we find four bosses in close proximity with one to two trash pulls between you and your kill. I'm going to go through these in order of difficulty.
Luckily for us, the easiest of the four is also the "last" boss you need to complete your Random. Rajh is a really straight forward fight with simple mechanics. There will be Cyclones creating fire paths in the room, avoid. Rajh will periodically cast Inferno Leap, if not interrupted, and jump towards a random Ranged target. If a flaming circle appears below you you will get a speed buff to help you dodge: take advantage of this and move. Summon Sun Orb brings an AoE bomb into the room, interrupt this cast or avoid the bomb if you fail to do so.
As he executes these, he's burning through "Sun Energy". When he hits 0 he's going to move to the middle of the room and begin channelling Blessing of the Sun to recharge; dealing AoE damage to everyone but taking 100% more damage during this phase. Everyone should stack on Rajh to make it easy to AoE heal and blow cooldowns during this phase to maximize damage. With sufficient DPS, you should only see one, maybe two, of these at most and be collecting loot.
You now have the option to take your Valour Points and scram, or step up to the remaining challenges.
It's really a toss up between which of the next two bosses is "easier", but lets go with Ammunae. This is a pretty straight forward tank and spank with a couple key complications.
Firstly, Ammunae will be spawning Seedling Pod's throughout the fight. These add a stacking HoT to the boss as they "grow" and will spawn additional adds if allowed to grow to fruition. They should be killed quickly because they get also gain increased health pools the longer they're allowed to grow; making them harder to kill. They can be hard to spot initially, but keep an eye out for a green dot hitting the floor, target it, and make it explode. She will hinder your ability to do this by casting Wither on random targets to reduce their attack/casting and movement speeds by 60%; this cast should be interrupted or dispelled.
Secondly, she'll occasionally spawn a Spore like the ones you killed in her trash. Kill them to eliminate their AoE proximity damage but remember to not stand in the void zone they create when they die. If you do get any Bloodpetal Blossoms, you can kite them through these patches to kill them quickly.
Keep up with the add spawns and you should find this boss to be no problem.
Next up is Isiset. She starts the fight with four abilities: Supernova, an announced AoE attack that works like the Radiance attack from Eadric in ToC in that it will stun you if you don't face away from the boss, Astral Rain, a constant cast similar to the Boomkin's Starfall, Veil of Sky, a damage absorbing shield that should be dispelled, and Celestial Call, which will summon 1-3 Star Shard adds that should be burnt down.
At 60% and 30% health Isiset will despawn and split into 3/2 mini-bosses: conveniently also named Astral Rain, Celestial Call, and Veil of Sky. You need to kill one of these bosses to exit the phase and, doing so, does two things. First, it eliminates the ability of the boss you kill from her repertoire and, secondly, it strengthens the remaining two abilities.
The safest kill order is Astral Rain (this gets seriously healing intensive if you leave it for last) -> Celestial Call -> Kill Isiset while dispelling the shield. Do this, and you should have no problems with the fight.
The last boss here is a straight up hardcore DPS execution test and there's no point in trying it unless you've got 3 competent DPS in the 8K range at least. Setesh is an odd fight whereby no one actually Tanks the boss. Instead, shortly after pulling he will begin moving around the room and opening portals through which adds will begin spawning and the responsibility falls upon the Tank to pick these adds up and the DPS to kill the boss before he, and the Healer, get overwhelmed.
Complicating this on Heroic, the Portals must be destroyed to stop mobs from spawning like the Lord Jaraxus fight in Trial of the Crusader Heroic. The quicker the better because, while you'll likely always get a Void Sentinel to be tanked, you really want to avoid the portals being open long enough for Void Seekers to spawn because they can negate any and all magic effects (ie: healing), through a channeled spell called Anti-Magic Prison. Cast this on a tank with multiple Sentinels and Void Wyrms on him and he's going to die fast so, if one of these does get through, kill it. Thus, the fight becomes a DPS priority test along the lines of Portal > Void Seeker > Boss and the DPS requirements aren't low so it's a pretty legitimate one.
Helping with this somewhat is the other primary mechanic you need to juggle appropriately. Setesh will periodically pause and cast Seed of Chaos to begin channeling purple/green Void Mines against anyone within 15 yards like those on the Krick + Ick fight in Pit Of Saron. Instinctively, you're going to want to get out of these but, getting hit by one gives you a buff that increases your damage from all attacks by 15K for the next 15 seconds. So, you're going to want to balance getting that buff and staying in range of the boss to attack with awareness of the damage that will come in if you sit in too many of them while also remembering your healer is kinda occupied with the tank and his ever increasing number of adds. Don't be the jerk that gets all huffy if you sit in too long and die from lack of heals when that number gets high. Juggling some defensive cooldowns is the best way to get you through this while staying on Satesh.
Other than that, Satesh will cast Chaos Bolts at random targets so there's another reason to not let your health situation get out of hand. This is the most challenging boss for DPS in the instance, and probably of the entire Dungeon Tier short of the execution mastery required for the last boss of Grim Batol, so if you can get him down you're getting to the point where you're introductory raid boss worthy.