Xel'anegh the Many

I'm surprised there is no strategy available yet, so I post mine (ILvl 607 frost mage with Brann as tank):

This boss consists of 4 tentacles, 3 smaller, 1 big one.
If I remember correctly, their hp pool in a lvl 10 delve is 18 mio, 24 mio, 28 mio and 160 mio.

For each smaller tentacle you kill, the big one gets a stacking debuff for receiving +100% dmg taken.
As the hp pools of the smaller tentacles are way less it is quite mandatory to kill them first.

There is one caster tentacle and 2 melee tentacles. The melees submerge and emerge at your position,
hitting quite hard after 1-2 seconds.

One tentacle casts fear, this should be interrupted. After killing the 3 smaller ones, the big one shouldn't be any problem.
After each tentacle killed, the fight gets more easy.

I typically try to burst down the eye tentacle ASAP as its mind flay spam is constant unavoidable damage and makes it harder to get out of range of the other tentacles due to the snare it applies (You really don't want to be tanking auto-attacks from all three tentacles for prolonged periods of time).

Aside from that you want to keep an eye on the maw tentacle's energy gauge and get ready to interrupt/CC its fear cast when it's nearing 100%. The energy abilities on the other tentacles are avoidable (A very narrow but painful line AoE for the lasher tentacle and a standard swirly spam AoE for the main boss) and mostly just give you a reprieve from their auto-attacks.

Brann getting KO'd is a bit of an inevitability due to the tentacles meleeing whatever is actually in range of them but as long as you keep moving you should be able to survive until he recovers provided the eye tentacle has been dealt with.

I created an account just to comment on this. TY, did this with ilvl 605 fire mage, killed the melee tentacle that casts fear first (has a stupid little face, best way I can describe it rn), caster tentacle, other melee one and the boss shortly after with no trouble. Once I get the 125 rep to upvote I'll be sure to come back and do that.