I recall seeing this scene on tv from the early 2000's. It was not from the movie Predator but it is similar. The creature came down from the sky and snatched this soldier up into the air. Next scene I remember was a bunch of military personnel being in this outdoor concrete camp and the creature coming back. Some minor details were they were in a jungle terrain and it was sunny out. The alien like creature from what I can remember was a cross between Jeepers Creepers and Predator.
Might you be looking for Code Red - The Rubicon Conspiracy as per 1990s film, knockoff of Alien and Predator franchises, included a jetpack and a fanged frisbee?
Code Red: the Rubicon Conspiracy is a 2001 TV movie aired by UPN involving a dishonorably discharged Army Lieutenant by the name of Peter Doyle (played by Brian McNamara) who is called in for a rescue mission regarding the Rubicon Station in the midst of Africa. His brother, James Doyle, may be the last remaining member of the last mission squad. He was also the reason for Peter's discharge, The Rubicon Station has a nuclear failsafe due to detonate in 20 hours if it's not reset and there are local rebels in play. Furthermore, Doyle quickly learns that some of his opposition is not from this planet, but not all of them are enemies.
There are two aliens, one reptilian in armor and one with tentacles that suck people dry. It's set in a jungle. The reptilian armored alien moves around with giant leaps, and I think there is at least one scene where he leaps in, grabs a soldier, than jumps out.
He was actually saving the soldier from the other alien, but the squad doesn't realize that until later when they find a way to communicate.