I know exactly which game you mean. I played it too as a kid, completed lots of levels, but never got to the end. I thinks it was called 'caverns', but I'm not 100% sure. I didn't find anything online, but that's no surprise, with keywords like caverns, arrow and dos game. :wallbash:
Edit : Found it on
XTC Abandonware, it's called "Caverns of Bob". Seems I wasn't far off, as the executable is actually called caverns.exe :brain: