These bosses do not share health and need to die at similar times, as when one reaches 1 health it will start a 10 second cast called Dark Reconstitution which will heal it back to full.
The main thing to pay attention to as a tank on this encounter is which boss has control of the Hivemind, at the start of the encounter this will be Tekris's Hivemind Control which will require you to stack both bosses together, after ~1:10 it will change to Ka'zir's Hivemind Control which will require you to keep both bosses at least 20 yards apart. If the condition of the Hivemind Control is not met, the bosses and all adds will be buffed with Shadow Veil reducing damage taken by 99%.
The Hivemind Control will change ~70s thereafter (cast sequencing can alter the time)
[Heroic] Devouring Frenzy - When the Hivemind swaps control it will deal Nature damage to all players every 0.5 seconds for 12 seconds, increasing by 15% each cast.
Nullification Blast - This is the main tank mechanic that Tek'ris has. It will display a Shadow cone on the floor in front of the boss and will begin its cast. You can move out of the cone. If you are hit by this you will receive the Nullification debuff which will deal ticking damage and reduce healing received by 50%.
Spawn Acidic Aqir - This is an additional add, however this one cannot be killed. Eggs will spawn around the room and shortly after an Acidic Aqir will spawn and roll to the other side of the room. If you are hit by these you will get the Corrosion debuff which deals Nature damage every 2 seconds and increases all damage taken by 25% for its duration.
Volatile Eruption - Whilst Ka'zir's Hivemind Control is active one Drone will transform into a Volatile Drone which increases its health by 150% and is immune to Crowd Control. It will cast Volatile Eruption over 20 seconds, if the cast is successful it will deal a lethal amount of Nature damage to the raid. This add appears on the boss frames also for ease of access. During this mechanic you should stack on this add and cleave from it rather than the boss.
[Heroic] Acidic Blood - When a drone dies it will leave a puddle on the ground which will deal large amounts of Nature damage to anyone who stands in it. These pools last for 1 minute. Aim to not have the drones too spread out when they die.
Shortly after the Drones spawn 3 Darters will spawn. They will go to a random location in the room and begin casting. They can be displaced, rooted and stunned. These should be bought to the boss and killed ASAP.
Psionic Resonance - This is the main cast which will deal a small amount of raid wide damage (however there are 3 of them so it builds up).
Corrosion - The damage taken increase is now 50% (up from 25%).
Spawn Acidic Aqir - Pools of Acid seep from the eggs before hatching. You will see a small green aura around them.
Tank Damage Profile
Ensure Ka'zir does not cast Mind-Numbing Nova
Ensure you are helping your DPS cleave as much as possible
Keep Tek'ris faced away from the group to ensure nobody gets hit by Nullification Blast
Leg Sweep is useful to stun all of the Aqir Drones together so they do not move and stop meleeing the raid
Ring of Peace is useful to control the Aqir Darters by placing it down as their cast finishes so they get knocked back to the group
Vengeance Demon Hunter
Sigil of Chains is useful to control the Aqir Darters by placing it down as their cast finishes so they get gripped back
Sigil of Chains can also be useful to grip all of the Aqir Drones together on top of the priority Drone (Volatile Drone, and in Heroic the Ravager Drone)
Sigil of Misery can stop the cast from the Aqir Darter therefore it will not move
Hammer of Justice is useful to stun the Aqir Darter to interrupt its cast and ensure it does not move
Avenger's Shield is very useful to solo the interrupts of Mind-Numbing Nova on Ka'zir
Shockwave is useful to stun the Darter to interrupt its cast and ensure it does not move
Shockwave can also be used to stun all of the Aqir Drones together so they do not move and stop meleeing the raid
Ursol's Vortex is useful to control the Aqir Darters by placing it down as their cast finishes so they get gripped back
Mighty Bash is useful to stun the Aqir Darter to interrupt its cast and ensure it does not move
Blood Death Knight
Death Grip is very useful to bring the Aqir Darter you are killing to the boss, so that cleave DPS is effective
Asphyxiate is useful to stun the Aqir Darter to interrupt its cast and ensure it does not move
Gorefiend's Grasp is useful to grip all of the Aqir Drones together on top of the priority Drone (Volatile Drone, and in Heroic the Ravager Drone)