Petrahydrox's ability triggers only if it's on the battlefield when it becomes the target of a spell or ability.

Petrahydrox's ability resolves before the spell or ability that caused it to trigger. It resolves even if that spell or ability is countered.

If the spell or ability that targets Petrahydrox has no other targets, it won't resolve (because it no longer has a legal target after Petrahydrox has returned to its owner's hand).