The tricky part is that the shareware demo version is absurdly hard to find. Simple Googling will overwhelm you with links to "abandonware" sites that offer the full version, and there are some old pages with outdated links to the shareware download that no longer work. Apparently, the shareware demo file, called SDRAMP.EXE according to such sources, used to be hosted at FileFront, but it isn't there anymore for some reason.
So far, I've been able to track down two places where the real shareware version of Alien Rampage can be found. First off, Demu.org (previously known as DOS Museum) has the shareware demo v1.0, without the installer. The other is much more obscure. It's the original installer of shareware demo v1.12, which was included on a cover CD of a Polish gaming magazine called CD Action. A copy of this CD got archived at cd.textfiles.com, and this is how the demo got on the net. The files are located here:
Luckily, Litude joined the search, and soon found and uploaded several original shareware files: