Worst Case for AVL Tree Balancing after Deletion
To make a lot of rebalancing, you would like to make your AVL tree as imbalanced as possible. And the worst case is a Fibonnachi-like tree:

, where $T_n$ is a tree with $T_{n-1}$ as a left child and $T_{n-2}$ as a right child ($T_1=T_2=$single-node tree).
On this example, if you remove 19, then node 18 must be rebalanced. After that, node 13 must be rebalanced. Essentially, you will have a rebalance at every level above node 20. You can build an arbitrary large such tree. I didn't check, but it should be simple to prove that removing the rightmost node always suffices for the worst case.