I think people are being quite unfair to the OP. The fact is there are some horses that are never quite right. It sounds like between the health and fear issues this filly will never have a good quality of life.
That said, being shot like a hunted animal would not be the way I would do it. Euthanasia by bullet is fine, but it needs to be done properly at close range. I would NEVER want to do it from a distance. Too easy to miss and have an injured animal that is in pain and panicked.
If you can top feed wormer paste, you can probably also top feed ace. Once she's sedated enough to catch and handle there are plenty of humane ways to euthanize.
A friend of mine had to euthanize her heart horse after repeated bouts of uveitis. He'd been a well socialized hunt horse but losing his vision repeatedly left him spooky and he became a danger to himself and others. This horse had every treatment recommended to him and he still could not be saved.