- Must be on GOG
- Must have achievements, if not on Galaxy then at least ingame
- Must have damage-over-time weaponry that you can always replenish ammo for before you run out. So, no disposable weapons and no having to rely on RNG to get one (as in most roguelikes)
- Can be any genre of twitch-based game. Twin-stick, fps, tps, whatever.
- Doesn't have to be a shooter. Can be a melee-oriented game instead.

Obviously the third criterion rules out almost everything. Out of my entire library all I could come up with was Terraria and Fallout New Vegas. And Ziggurat, if only the achievements weren't bugged for me. There's also Grim Dawn, but it kind of stretches what I'd consider a ''twitch'' game.

Deadpool 2013?

Edit: Nevermind, I don't think Deadpool is on GOG.

I'm not the biggest action game fan, but the Batman Arkham series is one of my my favorites. Rumors say that they'll be here "soon".
I also don't care much about achievements, but the in-game ones are really well-integrated into the games. They're a lot more than just "congrats, you've just achieved this".

What is a twitch game? A game with a lot of streaming time on twitch?

anyway i have outward in my lib... if fallout could pass i guess that one could pass this absurd demand too ;)

Twitch reflexes.

Ah oke such as those sweet 8 bit games that seem to be so popular now.... ITTA for example, or watched another promotional found in the head lights with similar play today named... down below ? or enter the gungeon ?

Those games fit "twitch reflexes" better then a Fallout

Shadow Warrior (2013) might be something for you.

I'm not sure if this meets your requirements, but it may be worth a look: Ruiner.

https://www.gog.com/game/ruiner