I don't understand. If you were to extract the largest element of the list, you'd make one pass and find it, even if the largest element is at the end. No need to sort the entire array here.
The same with finding the topN. Instead of keeping track of the largest element so far, you keep track of the largest N elements so far. If you do it in a heap, you can add an element, or remove the smallest element in O(log N) time. Still need one pass through the array. Don't have to sort the array. Note that if N equals the size of the list, you perform a sort in O(N log N) time. Which is optimal.