Holding priority, cast Dualcaster Mage by paying its mana cost.
When Dualcaster Mage enters, it triggers, copying Graceful Reprieve, with the copy targeting Dualcaster Mage.
Resolve the copy of Graceful Reprieve.
Holding priority, activate Shilgengar by sacrificing Dualcaster Mage.
When Dualcaster Mage dies, Graceful Reprieve triggers, returning Dualcaster Mage from your graveyard to the battlefield.
Repeat from step 3.
Resolve all Shilgengar abilities from step 5.
This clever loop hinges on a recursive exchange between the graveyard and the battlefield, starting by casting Graceful Reprieve to set up a safety net. When you drop Dualcaster Mage with flash, its entry trigger copies that spell to target the Mage itself, ensuring it can return whenever it hits the graveyard. That is where Shilgengar, Sire of Famine comes in: you can sacrifice Dualcaster Mage to Shilgengar's first ability to generate a Blood token, which simultaneously triggers the waiting Graceful Reprieve to bring the Mage right back to repeat the process. Because you can feed this cycle endlessly, Shilgengar lets you amass infinite Blood tokens while triggering creature enters-the-battlefield, leaves-the-battlefield, and death effects infinitely.