One of my books (below) has a picture of a very similar looking spider identified as a spiny flag spider, Alpaida cornuta, also from Costa Rica. I wasn’t able to find anything online though using either the common name or the scientific name. The World Spider Catalog doesn’t seem to recognize that name at all, but I saw two species there from Costa Rica, A. bicornuta and A. championi. Perhaps this is one of those.
Here’s a similar looking unidentified Alpaida from Ecuador, so I think the genus is probably correct.
Reference:
[book:1592234283]
Thank you for posting this, I have been looking to identify this species for awhile now myself. I became good friends with this species while staying very close to where this was taken. This is one of the shots of my friend: http://www.flickr.com/photos/61600824@N08/5601189779/
Looks like maybe your friend caught a fly. This species, whatever it is, does seem to be quite common in that area.