If you have any landscaping shops relatively nearby, so and get some big chunks of sandstone (or various other rock). We have almost exactly the same problem as you (neighbour's dog even looks the same xD), a big hole in the retaining wall where the dog could almost get through. Thankfully it was non-aggressive.
We solved it by going down to the landscaping shop and just getting some large stones, and then we dumped them in the hole. The dog definitely can't push them over, and it'll learn quick smart if it tries to dig under them