A Tour of Towers

The quests and what class can run them (ref https://www.wowhead.com/mage-tower-building):

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• Closing the Eye - frost death knight, havoc demon hunter, survival hunter, subtlety rogue, arms warrior
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• The God-Queen's Fury - arcange mage, ret paladin, assassination rogue, enhancement shaman, demonology warlock
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• The Highlord's Return - blood death knight, vengeance demon hunter, guardian druid, brewmaster monk, protection paladin, protection warrior
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• Thwarting the Twins - balance druid, marksman hunter, frost mage, shadow priest, affliction warlock
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• An Impossible Foe - unholy death knight, feral druid, fire mage, outlaw rogue, elemental shaman, fury warrior
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• Feltotem's Fall - beast mastery hunter, windwalker monk, discipline priest, destruction warlock
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• End of the Risen Threat - restoration druid, holy paladin, holy priest, restoration shaman, Mistweaver Monk
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Here's a script to check the achievement progress. Hopefully I got the order right. The criteria are hidden ingame and don't have names.

/run for i=1,7 do local p,_,_,c=string.char(124),GetAchievementCriteriaInfo(15310,i,true) print(({'Xylem','Agatha','Sigryn','Tugar Bloodtotem','Kruul','Heal','Twins'}), c and (p..'cff00ff00done'..p..'r') or (p..'cffff0000not done'..p..'r')) end


I've created a document that lists all possible main and alt class combinations while still maintaining a maximum amount of three characters. It's a cheat sheet for what alt classes to gear up, or which alt classes to create, so you can obtain the mount with as less effort as possible. This should come in handy once the mage tower becomes available on the PTR and people can start making preparations for the live version.

You can find the document here.