Activate Cauldron of Souls by tapping it, giving Gerrard persist until end of turn.
Activate Extruder by sacrificing Cauldron of Souls, putting a +1/+1 counter on Gerrard.
Activate Goblin Bombardment by sacrificing Gerrard.
When Gerrard dies, it and its persist ability trigger.
Resolve the Gerrard persist trigger, returning it from your graveyard to the battlefield with a -1/-1 counter on it.
Resolve the second Gerrard trigger, failing to exile it as it has left your graveyard, and returning Cauldron of Souls from your graveyard to the battlefield.
Resolve the Goblin Bombardment ability from step 3, dealing 1 damage to any target.