Worst Case for AVL Tree Balancing after Deletion

After deleting a node in an AVL tree, self-balancing (zig-zag rotation or the left-right balancing) maintains O(logn) time that is not guaranteed in other unbalanced trees (like BST).

The Balancing operation is said to be O(1).

What is the worst case for balancing?

Any specific type of tree providing the worst case?