DoomWood
Quests
Everyone
Complete the DoomWood storyline. This includes: /lightguard > /doomwood > /maul > /necrotower > /necrou > /temple > /shadowfallwar > /lab > /mountain > /vordredboss > /necrodungeon > /necrocavern.
Complete the Zombies storyline. This includes: /doomhaven > /doomwar and /yulgarzombie (if member)
Complete the storyline from /thorngarde > /stonewood > /techdungeon > /stonewooddeep > /techfortress.
Member
If you're in a group, complete GrimDawn/Dusk's "Executive Doom OverLord Challenge" quest from /necrodungeon by defeating the Doom Overlord in the same map.
Otherwise, complete Yulgar's "Free Us, Oh Brave One!" quest from /yulgarzombie by defeating the Dark Dracozombie in the same map.
Requires completing Yulgar's previous quests and keeping the reward (the enemies for the previous quests are located at /templeb > /battleunderb > /doomwar).
Non-Mem
If you're in a group, complete GrimDawn/Dusk's "Doom OverLord Challenge" quest from /necrodungeon by defeating the Doom Overlord in the same map.
Otherwise, complete "Minion Morale", "Shadowfall is DOOMed", and "Grave-lyn Danger" quests from /shadowfall (click the Quests button at the top-right). You have to accept each of them separately from each screen in the map but then you can complete them all in the same room - I suggest the one with 2 Undead War Mages and 2 Ghouls.
Also make sure to enable Quest Log Turn-Ins and Reaccept Quest After Turn-In from Advanced Options. This way you can keep your Quest Log open and turn in quests from there. You can access your Quest Log by pressing L.