When you cast this spell, destroy target permanent. Indestructible Annihilator 4 When Ulamog, the Infinite Gyre is put into a graveyard from anywhere, its owner shuffles their graveyard into their library.
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 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.
Lethal damage and effects that say "destroy" won't cause a creature with indestructible to be put into the graveyard. However, a creature with indestructible can be put into the graveyard for a number of reasons. The most likely reasons are if it's sacrificed, if it's legendary and another legendary creature with the same name is controlled by the same player, or if its toughness is 0 or less.
Ulamog's ability triggers as you cast it, and that ability resolves before the spell itself. It resolves even if that spell is countered.