Nazgûl Battle-Mace

If an opponent sacrifices a nontoken permanent as part of paying the cost of a spell or ability, the last ability granted by Nazgûl Battle-Mace will trigger and go on the stack on top of that spell or ability. The ability granted by Nazgûl Battle-Mace will resolve before that spell or ability.

The last ability granted by Nazgûl Battle-Mace triggers whenever an opponent sacrifices a nontoken permanent for any reason, not just due to the annihilator ability.

Annihilator abilities trigger and resolve during the declare attackers step. The defending player chooses and sacrifices the required number of permanents before they declare blockers. Any creatures sacrificed this way won't be able to block.

If an opponent sacrifices a nontoken permanent, it doesn't matter which graveyard it goes to. The last ability granted by Nazgûl Battle-Mace will trigger.

If a replacement effect, such as that of Rest in Peace, causes a sacrificed nontoken permanent to be put into a different public zone than a graveyard, the last ability granted by Nazgûl Battle-Mace will still trigger and you will still put the card onto the battlefield under your control if its original controller doesn't pay 3 life.

If a creature with annihilator is attacking a planeswalker, and the defending player chooses to sacrifice that planeswalker, the attacking creature continues to attack. It may be blocked. If it isn't blocked, it simply won't deal combat damage to anything.