I was also looking for an answer to this question, but the only way to know it is to try to unlock at least one achievement, in fact there are two cases:
1) Invisible achievement bug: sometimes developers forget to make the achievement list visible once the game is launched on the store. In that case, the achievements appear gradually as they are unlocked. Recent example: Horace. With a few clicks the GOG staff or the game developers can correct this error.
2) GOG has put a wrong tag on the game page. Note that the profile page shows the achievement percentage of a game automatically if that game has the tag "achievements" so it can't help to understand if a game really has achievements.

Since Spiderweb Software has always refused to add achievements to Galaxy I'm leaning towards hypothesis 2, but we need a definitive confirmation. It could also be that they plan to add them later.

Hello,
Here is a quote from the developer responding on Steam.


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OK. I just rebuilt the Windows version and I checked the achievement code very carefully. I hotfixed the patch to Steam, downloaded it on a test account, and achievements are being awarded correctly. (Version number on title screen will be v1.0b).

The game will be smart enough to tell what medals you've already gotten and give you the achievements now, so you won't lose anything.

If you're using Windows and try it and it works, please let me know. Then I can stop worrying. :)
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Here he is only referring to the Steam version and not the GOG Galaxy achievements unfortunately.
Someone could try to contact the developers on Steam since they never show up on GOG.

Interesting, I never saw 1) before. Horace indeed has achievements but they are not showing up on the list. Good to know that this could happen.

I just tested the game and completed the tutorial. I got the in-game medal but no achievement. I tried on both Windows and Mac. It could also be a third alternative: maybe the achievements are invisible AND the game has a bug here like it did on Steam, but I'm also leaning towards 2) based on all other Spiderweb games here.

I've reached out to GOG support a couple of days ago but no answer so far. I'll try to reach out to Spiderweb directly to confirm.

GOG support just replied. In fact, the game doesn't support GOG achievements. They also fixed the store page information.

Thanks for the update on the situation, shameful that Spiderweb Software never deigns to add Galaxy achievements to its games on GOG. As far as I'm concerned their games are blacklisted until they change their attitude.