Be Our Guest

Each guest has a specific one of the four slots that they will show up in. Below is a list taken from the Wowpedia Ember Court page:

Slot 1:

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• Cryptkeeper Kassir
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• Plague Deviser Marileth
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• Choofa
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• Sika
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Slot 2:

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• Stonehead
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• Droman Aliothe
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• Grandmaster Vole
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• Kleia and Pelagos
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Slot 3:

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• Rendle and Cudgelface
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• Alexandros Mograine
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• Hunt-Captain Korayn
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• Polemarch Adrestes
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Slot 4:

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• The Countess
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• Baroness Vashj
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• Lady Moonberry
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• Mikanikos
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The new achievement Shadowlands Dilettante coming with 9.2.5 will require this achievement, which itself is part of the new meta-achievement Back from the Beyond. This list will help with how many weeks are needed to complete this achievement, as even having only 4 guests remaining might require multiple weeks if they show up in the same slot.

As noted in other comments, the slots unlock with the relevant level of the Ember Court (i.e. level 1 unlocks slot 1, level 2 unlocks slot 2, etc.) so this achievement requires level 4 to be able to invite the guests listed under slot 4. Level 5 of the Ember Court is not needed for this achievement, as level 5 is only a happiness boost to guests and this achievement simply requires running the Ember Court with each guest at least once.

Im suprised no one mentioned this yet, but court can now be done daily instead of weekly as of 10.2, so if you know what you are doing this achievment is now duoble in less than a week, provided you have ember court on level 4, that is a must for the achievment. I also suggest setting aside an hour of your time to research how court works, as that can save you day or two in itself.

What other comments fail to note is that this achievement requires honored with the Ember Court in order to purchase the RSVP for Choofa. Therefore, if you do the bare minimum and fail to get the maximum 1600 rep a week it may take more then 4 or 5 weeks implied elsewhere. Subsequently, it may be prudent to put moderate effort in to make sure grinding the reputation does not that too many weeks.