Activate Shilgengar by sacrificing another creature.
When the creature dies, Bishop of Wings' second ability triggers, creating a 1/1 Spirit creature token.
When the Spirit token enters the battlefield as an Angel due to Conspiracy, Bishop of Wings' first ability triggers, causing you to gain 4 life.
Resolve the Shilgengar ability.
Repeat.
This loop is all about a clever identity crisis engineered by Conspiracy, which redefines every creature you own and control—including tokens—as Angels. With that blanket type-shifting in place, whenever Shilgengar, Sire of Famine sacrifices a creature to generate Blood tokens, its death immediately triggers Bishop of Wings to spawn a 1/1 Spirit token. Because Conspiracy turns that fresh token into an Angel the moment it hits the board, Bishop of Wings triggers a second time to pad your life total by 4. You can then feed those newly minted Blood tokens back into Shilgengar, Sire of Famine to mass-reanimate your graveyard and keep the cycle spinning infinitely.