The premise of my story is somewhat similar to Jurassic Park in that a creature needs to be replicated from very little remaining organic matter. 

In this case, though, the relevant material is not found in fossilized bugs but from a recently deceased specimen. Is there any issue with the amount of matter or is a handful of cells enough?

Assume that nothing damaged the DNA of the specimen. Essentially the prospective cloners came across the creature after having been fed on by scavengers leaving very little left.

*Note: the cloning technology in question is alien so there is some leeway if necessary*