Does a spell that says 'destroy target creature' kill an indestructible creature if it also has a -1/-1 counter effect attached?

Indestructible is a static ability that means the permanent cannot be destroyed — specifically, it is not destroyed by effects that say 'destroy' and is not destroyed by lethal damage (CR 702.12b). So the 'destroy target creature' portion of a spell will simply fail to destroy an indestructible creature.

However, if the same spell or effect also places -1/-1 counters on that creature, those counters reduce the creature's toughness. If the creature's toughness is reduced to 0 or less, it is put into its owner's graveyard as a state-based action under CR 704.5f. This is not destruction — it is a toughness-based state-based action — so indestructible does NOT protect against it.

The two parts of the effect are independent. Indestructible only shields the creature from the word 'destroy' and from lethal damage; it provides no protection against toughness being reduced to 0 or less, or from being sacrificed, exiled, or other non-destroy removal.

Example: Your opponent controls a 4/4 indestructible creature. You cast a spell that says 'Destroy target creature, then put four -1/-1 counters on it.' The destroy instruction does nothing (indestructible), but the four -1/-1 counters make it a 0/0. State-based actions then cause it to be put into the graveyard (CR 704.5f) — not because it was destroyed, but because its toughness reached 0.

So the verdict: the 'destroy' text is blanked by indestructible, but a separate -1/-1 counter effect on the same spell can still kill the creature if toughness drops to 0 or less.