Is there a possibility to get the Game from the Cyanide-Shop running in Steam and getting the achievements there?

Question still waiting for an answer

no
get from steam then you can get achievements
get from the Cyanide-Shop and you can not get achievements

Note that if you do get another copy of the game from Steam, you will not get the Steam achievements you have already earned (unless Cyanide fixes their code). See here: viewtopic.php?f=13&t=534

To get all Steam achievements you must create a new coach name and not play with the same name you use with the Cyanide-bought game. That will maybe work, haven't tried it myself.

To get all Steam achievements you must create a new coach name and not play with the same name you use with the Cyanide-bought game.

I tried it and it actually works. See here: viewtopic.php?f=13&t=534&p=3021#p3021