I can collect the achievements just fine, but when I quit the game they are not saved.
So, when I restart the game, all achievements are gone.

(I also tried to start the game as an administrator, bu that doesn't help.)

Does someone else has this problem?

Same problem here :(

Yes, same problem with the Linux build here. Between game restarts things seem to get forgotten. Or randomly, after finishing an episode. That pretty much sucks. I just finished ep. 1 with a good bunch of them received and now, the table it entirely empty. Also reloading a ep1 save won't bring this back, so I guess the achievement table is handled separately, which makes sense.
But it seems it get forgotten for some reason.

gameinfo has
Secret Agent HD
v1.0.5

Bumping this thread. Same thing has happened to me.

I recently started playing Secret Agent HD (I hope this is the right forum?). Suffering the same problem as the users above, achievements are not getting saved/granted in GOG but plop up in game.

Edit:
Suddenly, it works. Was it a fast fix or was there something going on on my end?

Same thing here. I noticed after completing Episode 1 and coming back later to start the second. I think the ones I had already earned stayed showing until the end of the episode (completed over a few days, not in one sitting), but I wasn't paying enough attention to it to say for sure.

I'm on the latest version 1.0.5, playing offline without Galaxy. Previously I played Crystal Caves HD (appears to be the same engine) and didn't have this issue.