Ivy is certainly a hot topic of debate. It's considered invasive and has been banned in some States. Also, some landscaping companies have taken a "No Ivy" pledge.
There's even a website (that might have some answers for you, I haven't completely checked it out), called the ~Ivy Removal Project~ . Take a look, when you have a couple of minutes.
I don't know how you feel about using a product like Roundup, and have read varying reports about whether or not it penetrates the waxy leaves, or if you need to spray the undersides, etc., but other than that, back breaking work with a pick axe and shovel may be your only choice. Doesn't sound like much fun, does it?
Thanks for the welcome! Yes, it doesn't sound like much fun. I use roundup alot, but may not want to closer to the pond.
I will try it and let you know and I will also check out the website too.