Can this anime be identified by a small number of disconnected scenes?
That sounds almost exactly like IRIA: Zeiram the Animation to me. (http://www.imdb.com/title/tt0107228)

I really loved Iria when it first came out, the action and character designs are excellent. Interestingly, this OVA is based on a live-action movie series called Zeiram (which I've never seen). I wish they had made sequels to this anime because I found Iria a pretty engaging character at the time (haven't seen it in forever). Her grappling hook thing was pretty slick and she kicked serious butt ;)

The alien (Zeiram) is pretty much unstoppable and has a creepy, extensible face (kind of like a Xenomorph). It can clone itself and absorb people. Here's the description of the monster (from http://myanimelist.net/character/21662/Zeiram#aJugBUYj0dqWceUH.99):


  "Zeiram is the ultimate being and virtually indestructible. In addition to being 
  extremely powerful, Zeiram can generate imperfect clones of itself to assist in battle. 
  Zeiram also needs to assimilate other life forms in order to sustain itself, but in 
  doing so it is thought that Zeiram can learn whatever is known by the organism being 
  assimilated. Zeiram is not a unique creature and other versions of itself are known to 
  exist throughout the universe. Later in the show Zeiram attempts to contact other 
  Zeirams in order to bring them to Myce."


Hope that helps!