Acererak the Archlich

When Acererak enters, if you haven't completed Tomb of Annihilation, return Acererak to its owner's hand and venture into the dungeon.
Whenever Acererak attacks, for each opponent, you create a 2/2 black Zombie creature token unless that player sacrifices a creature of their choice.

Dungeon Master's Guide, *5th Edition (2014)*

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Acererak the Archlich has an intervening if clause in its first triggered ability. If you have completed Tomb of Annihilation, the ability won't trigger at all. If it does trigger, but you somehow complete Tomb of Annihilation while the ability is on the stack, then the ability won't do anything. You won't return Acererak to its owner's hand and you won't venture into the dungeon.

If Acererak is no longer on the battlefield as its first ability resolves and you haven't completed Tomb of Annihilation, you will still venture into the dungeon.

In a multiplayer game, each opponent decides in turn order whether or not they will sacrifice a creature and which one they will sacrifice. Each opponent knows the choices made before they make their own choice. Then, once all opponents have chosen, creatures are sacrificed and tokens are created simultaneously.

Zombie

Dungeon of the Mad Mage

Yawning Portal — You gain 1 life. (Leads to: Dungeon Level)
Dungeon Level — Scry 1. (Leads to: Goblin Bazaar, Twisted Caverns)
Goblin Bazaar — Create a Treasure token. (Leads to: Lost Level)
Twisted Caverns — Target creature can't attack until your next turn. (Leads to: Lost Level)
Lost Level — Scry 2. (Leads to: Runestone Caverns, Muiral's Graveyard)
Runestone Caverns — Exile the top two cards of your library. You may play them. (Leads to: Deep Mines)
Muiral's Graveyard — Create two 1/1 black Skeleton creature tokens. (Leads to: Deep Mines)
Deep Mines — Scry 3. (Leads to: Mad Wizard's Lair)
Mad Wizard's Lair — Draw three cards and reveal them. You may cast one of them without paying its mana cost.

Lost Mine of Phandelver

Cave Entrance — Scry 1. (Leads to: Goblin Lair, Mine Tunnels)
Goblin Lair — Create a 1/1 red Goblin creature token. (Leads to: Storeroom, Dark Pool)
Mine Tunnels — Create a Treasure token. (Leads to: Dark Pool, Fungi Cavern)
Storeroom — Put a +1/+1 counter on target creature. (Leads to: Temple of Dumathoin)
Dark Pool — Each opponent loses 1 life and you gain 1 life. (Leads to: Temple of Dumathoin)
Fungi Cavern — Target creature gets -4/-0 until your next turn. (Leads to: Temple of Dumathoin)
Temple of Dumathoin — Draw a card.

Tomb of Annihilation

Trapped Entry — Each player loses 1 life. (Leads to: Veils of Fear, Oubliette)
Veils of Fear — Each player loses 2 life unless they discard a card. (Leads to: Sandfall Cell)
Sandfall Cell — Each player loses 2 life unless they sacrifice a creature, artifact, or land of their choice. (Leads to: Cradle of the Death God)
Oubliette — Discard a card and sacrifice a creature, an artifact, and a land. (Leads to: Cradle of the Death God)
Cradle of the Death God — Create The Atropal, a legendary 4/4 black God Horror creature token with deathtouch.