I spent a lot of time yesterday looking into this because I wasn't seeing them proc either. It looks like Ys I&II don't have GoG Galaxy integration, but the achievements still show up on the game's page in my library anyway, which is weird.
I've had odd experiences with achievements for a game in Steam proc'ing when I was playing a GoG version of the game. This happened several times when playing Legend of Heroes: Trails in the Sky with both the Steam client and GoG Galaxy open.
On a hunch I tried opening Steam to see if that would help for some unknown reason. It didn't, but then I tried installing and playing the Steam version while the Galaxy client was open and Ys I was installed. With this setup, whenever I get an achievement in Steam, I also get the corresponding achievement in GoG once I close the game.
My best educated guess is that since I own the game in both ecosystems and I've linked my steam account to my GoG account for the GoG Connect games, GoG can read my Steam achievements via an API and say I have them here. Unfortunately my only evidence is circumstantial.
alexandros050: Does anyone know if achievements work for the other YS Games? If not maybe we should send a message to xseed support. Maybe they will fix them if they can.
As for achievments in other Ys games, I've played both Oath in Felghana and Memories of Celceta through the Galaxy client and had achievements proc with both games as you would expect them too. My suspicion is that Ys I&II are the exceptions rather than the rule. They are the only Ys games that do not advertise achievement support in the "Game Features" section of the sidebar on the store page.
tl;dr:
If you own a copy on both GoG and Steam, play the steam version with the Galaxy client open and see if that works. If you don't own both copies, try sending a support ticket to GoG (send it as a Galaxy-related bug, not an Ys-related one) and maybe they can at least explain why the achievements are visible if they aren't explicitly supported.
