Ys Origin has some, but it's missing most of them, most notably anything related to the boss rush. Hopefully it's just the achievements that are missing and not the boss rush itself.
At least when I played it, the boss rush was, indeed, present.
With that said, on my setup (playing the game through Wine on Linux), the game would likely crash when running the entire boss rush before it could save a time. Then again, because it takes so long, I find it more fun to just play individual bosses.