Doesn't look too bad. I'd personally go with a wood slat fence, but that is just my preference. I'd look at the ancient fence next door to check for movement, as it doesn't look like it's gone anywhere. I don't think I'd be worried about erosion at all.

Here is the thread from when I built a wall under my fence. https://www.ar-15.co/threads/154827-...retaining+wall

Honestly, I probably wouldn't even bother doing anything with yours beyond building a little trench (6"-12") and burying the chain link in the trench. Just make sure that you get a fence tall enough that burying it isn't going to make it too easy for the pups to jump the top.