Not yet, you will supposedly be able to do so later. Galaxy features aren't being rolled out quickly. ;)

Are we talking about an in-game feature, or Galaxy achievements? In-game achievements probably can't be disabled, but it would depend on the game. Galaxy achievements still can't be turned off last I heard, but you can choose to play without Galaxy. Make sure you log out before closing Galaxy though, since for some reason just closing it can leave you logged in and cause you to gain achievements even without the client running.

Yeah, GOG intends to make all of these features available as "optional" as advertised for 2+ years now, but what's not known is when that is planned to actually happen. There are some checkboxes to turn some features off in the settings pane, but it is a non-functional mockup that they haven't attached the checkboxes in there to actual code that does anything yet.

Talking about Galaxy axchievements.
I keep away from steam because, except for setting my profile private, there is no way to totally deactivate achievement system.
Not only hate people to compare/judge my game "completion", but also feel forced to play it as other people want me to, not as I like.
The existence itself of gog galaxy achievements hurt me (ocd, already diagnosed, no irony plz), because i feel compelled to complete it, and feel a pain all the way through, not enjoying the game itself.

So, galaxy achievs can't be disabled?

Not yet.
Remember Galaxy is still in beta, it's a feature that they announced though.
You'll be able to disable them eventually.

You could uninstall galaxy... Not sure if you don't have to reinstall the game though from the installers.

1) Ignore other people and be proud to be who you are.

2) Download GOG games through browser, there's absolutely no way for any achievements to work then.
Yes, sometimes there may be some stupid popups in game telling about you "achieving" something, but nothing will be recorded to any database or shown publicly.

finally, I can disable time played & achievements.
Ty so much, devs

I HATE being told how much time I have been playing!!!

"You know you don't have a life, but just to make it official, we are giving you documented proof of it."

:D

There used to be some games -- mostly Japanese-made console games, as far as I know -- which would actually remind you every once in a while that you'd been playing for a long time. In Rogue Galaxy, for instance, some of the companion characters would occasionally say throw out random lines of spoken dialogue along the lines of "You've been playing for an awfully long time...maybe you should take a break."

Get your gOgs outside of Galaxy, like PixelBoy said.
It's not hard to avoid achievements, most games don't have them.
See this list:

https://www.gog.com/games?feature=achievements&sort=bestselling&page=1