Achievements of "The Trouble With Clones" and "Gangstas in Space" don't seem to work, for example klling 15 cameramen, melee killing 15 cops at the strip club, shooting fans with bees etc. Anyone else has this problem? Any solutions?

Yes, it's a fact that many SR3 Remastered achievements don't work. The only thing you can do is to contact GOG support so that they contact the developers and possibly also try to contact those incompetent people at Deep Silver, although their support seems non-existent at the moment. In case, let me know if they reply.