at the top of one's voice; as loudly as possible
Fixed adverbial phrase used with verbs of shouting, crying, or calling to mean using one's full voice.
He shouted for help at the top of his voice.
The child is crying as loudly as possible.
A fixed expression combining 声 (voice), the object marker を, and 限りに (to the limit of), literally 'to the limit of one's voice'.