You can install Gnome 3.8 Shell in LMDE, but you have to get it from the Debian Experimental
repo. This can be hazardous to your system, unless you know what you are doing and take care. Right now LMDE Gnome Shell is at 3.4. Unless you are really experimental, I would stick with 3.4. There are many extensions available for it.https://extensions.gnome.org/#sort=recent
There are less than a handful availble for 3.8. To me the right extensions are very necessary. I went to 3.8, but went back to 3.4 because of it.
If your determined to go to 3.8, you can learn a lot in this thread. Its very long, but lots of valuable info.viewtopic.php?f=201&t=65745
It's safe to use JHBuild?
If you are going to compile from souce, your on your own....