Holding priority, cast Dualcaster Mage by paying its mana cost.
When Dualcaster Mage enters, it triggers, copying Reincarnation, with the copy targeting Dualcaster Mage.
Resolve the copy of Reincarnation.
Holding priority, activate Shilgengar by sacrificing Dualcaster Mage.
When Dualcaster Mage dies, Reincarnation triggers, returning Dualcaster Mage from your graveyard to the battlefield.
Repeat from step 3.
Resolve all Shilgengar abilities from step 5.
This loop hinges on a clever recursive engine powered by Dualcaster Mage and Reincarnation to perpetually trigger entering-the-battlefield and death events. By targeting Dualcaster Mage with the copy of Reincarnation it generates upon entry, you set up a loop where sacrificing the Mage to Shilgengar, Sire of Famine's activation cost immediately triggers its return from the graveyard. Meanwhile, Shilgengar, Sire of Famine feasts on the sacrifices to flood your board with an endless horde of Blood tokens, which can eventually be cashed in to mass-reanimate your entire graveyard with finality counters.