Cast Persist by paying its mana cost, targeting any applicable target.
Holding priority, cast Dualcaster Mage by paying its mana cost.
When Dualcaster Mage enters, it triggers, targeting Persist.
Holding priority, activate Altar of Dementia by sacrificing Dualcaster Mage.
Resolve the Dualcaster Mage trigger, copying Persist, with the copy targeting Dualcaster Mage
Resolve the Persist copy, returning Dualcaster Mage from your graveyard to the battlefield.
Repeat from step 3.
This loop transforms a simple graveyard recursion spell into an infinite engine by leveraging Dualcaster Mage's clever habit of copying spells on the stack as it enters the battlefield. By pointing the newly minted copy of Persist back at Dualcaster Mage itself—which you conveniently feed to Altar of Dementia just before the copy resolves—you create an endless cycle of sacrifice, resurrection, and spell replication. Altar of Dementia harnesses this perpetual motion to mill out your opponents completely, while also generating an endless stream of death, entry, and leave-the-battlefield triggers to fuel any other synergies you might have on the board.