I have installed batman arkham asylum in steam but not launching
I have it working. I actually have played this one on Windows, BUT:
First provide your system information at minimum: How to provide good information
Also verify your files through Steam: Verify Integrity of Game Files - How To's - Knowledge Base - Steam Support
According to Proton DB:
As others have reported, just run the below in terminal (pointing at your Steam library prefix for the game) to launch and play successfully:
WINEPREFIX=$HOME/steamapps/compatdata/35140/pfx winetricks mdx d3dx9 d3dcompiler_43 win10
Without the above (or equivalent using protontricks), the settings launcher will appear but will throw a shader compiler error on play.