A Distraction for Akama

This quest is pure script, you do not need to take any action. Once you have accepted the quest, talk to Xi'ri again.

Quest still works in Shadowlands, although it appears to be a bit buggy, and for a moment I thought it was broken.

Talk to Xi'ri and say you're ready to join the attack. There will be a message in the chat log saying Xi'ri is making a decision. After about 30 seconds, Xi'ri starts casting a buff spell which takes a moment, then once done you can help the Aldor and Scryer NPCs kill the demons outside Black Temple. Akama and Maiev and the Deathsworn might not be there yet, but you can still proceed. Once you kill all the demons outside the temple, another wave will eventually spawn after a moment, with a Dreadlord called Vagath at the end. It seems like he can't die until a certain event occurs, and just stays at 1% HP while you attack him.

Soon you should see Maiev Shadowsong and Akama start yelling in the chat log, and a moment later Vagath finally died. If you run back to Xi'ri, Akama and Maiev's forces should be there. After about 20 seconds of them doing nothing, Akama says "We must carry on with or without Maiev. Inside! Quickly!", but nothing seems to happen. Then a moment later, the Deathsworn NPCs and Akama just despawned. I ran towards the Black Temple entrance, and saw Akama running into the raid portal, then the objective completed and you can turn it back in to Xi'ri and pick up the next step.

This is a quest involved in the Black Temple Attunement Chain:

The Black Temple attunement starts at The Altar of the Sha'tar for Aldors, and the Sanctum of the Sun for Scryers. Both are in Shadowmoon Valley.

Aldors start attunement from Anchorite Ceyla (http://www.wowhead.com/?npc=21402) at the Altar of Sha'tar in Shadowmoon Valley:
1. [A] http://www.wowhead.com/?quest=10568 [70] Tablets of Baa'ri
2. [A] http://www.wowhead.com/?quest=10571 [70] Oronu the Elder
3. [A] http://www.wowhead.com/?quest=10574 [70] The Ashtongue Corruptors
4. [A] http://www.wowhead.com/?quest=10575 [70] The Warden's Cage

Scyers start attunement from Arcanist Thelis (http://www.wowhead.com/?npc=21955) at the Sanctum of Stars:
1. [Sc] http://www.wowhead.com/?quest=10683 [70] Tablets of Baa'ri
2. [Sc]http://www.wowhead.com/?quest=10684 [70] Oronu the Elder
3. [Sc] http://www.wowhead.com/?quest=10685 [70] The Ashtongue Corruptors
4. [Sc] http://www.wowhead.com/?quest=10686 [70] The Warden's Cage

After that, the chain comes together for Aldor and Scryer.

5. http://www.wowhead.com/?quest=10622 [70] Proof of Allegiance
6. http://www.wowhead.com/?quest=10628 [70] Akama
7. http://www.wowhead.com/?quest=10705 [70] Seer Udalo

Seer Udalo is found in the Arcatraz (http://www.wowhead.com/?zone=3846) just before the last boss.

8. http://www.wowhead.com/?quest=10706 [70] A Mysterious Portent
9. http://www.wowhead.com/?quest=10707 [70] The Ata'mal Terrace
10. http://www.wowhead.com/?quest=10708 [70] Akama's Promise

After you finish this chain, you get to pick from some rewards and the chain seems like it ends. It continues however, inside Serpentshrine Cavern (http://www.wowhead.com/?zone=3607) from an NPC called Seer Olum (http://www.wowhead.com/?npc=22820) who you can speak with after killing Fathom-Lord Karathress. He starts the next part of the Black Temple Chain by offering the quest:

1. http://www.wowhead.com/?quest=10944 [70] The Secret Compromised
For this quest you just return to Akama.
2. http://www.wowhead.com/?quest=10946 [70] Ruse of the Ashtongue
In this quest, you must use the costume Akama provides, and kill A'lar in Tempest Keep: The Eye while wearing the Ashtongue Cowl. Attunement for The Eye is a whole different chain.
3. http://www.wowhead.com/?quest=10947 [70] An Artifact From the Past
In this, you need to gain access to The Battle of Mount Hyjal in Caverns of Time, and slay the first boss, Rage Winterchill. Attunement for this involves killing Lady Vashj and Kael'Thas Sunstrider.
4. http://www.wowhead.com/?quest=10948 [70] The Hostage Soul
For this you must speak with A'dal in Shattrath city.
5. http://www.wowhead.com/?quest=10949 [70] Entry into the Black Temple
For this, just speak with the naaru Xi'ri in front of Black Temple.
6. http://www.wowhead.com/?quest=10985 [70] A Distraction for Akama
Unknown what this quest asks of you, most likely you need to defend Xi'ri and make your way into Black Temple. At the end, you become attuned to enter and are granted The Medallion of Karabor (http://www.wowhead.com/?item=32649)

At this point, you are attuned and can enter Black Temple, although the chain continues and you can soon upgrade your medallion. It continues with:

1. http://www.wowhead.com/?quest=10958 [70] Seek Out the Ashtongue
You just need to find Seer Kanai (http://www.wowhead.com/?npc=23158) inside Black Temple.
2. http://www.wowhead.com/?quest=10957 [70] Redemption of the Ashtongue
This involves entering Black Temple, and killing the boss the Shade of Akama (http://www.wowhead.com/?npc=22841).
3. http://www.wowhead.com/?quest=10959 [70] The Fall of the Betrayer
After killing the Shade of Akama and returning to Seer Kanai, he asks one last thing of you. Kill Illidan The Betrayer. After doing so, you are granted the Blessed Medallion of Karabor, an upgraded version of your original medallion, and allows teleportation to the Black Temple.