The plot, in general, is simple: the CIA terminates the Operation Outcome program—and literally—its trained agents Jason Bourne (Matt Damon) and Aaron Cross (Jeremy Renner), and everyone else who has knowledge of it. This includes Dr. Marta Shearing (spectacularly played by Rachel Weisz), one of the scientists who provide the agents with performance-enhancing drugs.
This whole drama unfolds in the same timeline as Bourne Ultimatum, the third and preceding film in the Bourne franchise, so I highly suggest you watch Ultimatum first (or at least, read the Wikipedia entry) for you to get the many cross-references.
I was just warming up to this premise at its two-and-a-half-hour mark when the first few notes of the theme song, normally signalling the end credits, began playing. Wait, the movie's over?! As a matter of fact, it was, and other members of the audience felt the same as I observed and heard them from my seat. (Pam, in her case, was waiting for Edward Norton's character, the main antagonist, to fly to Manila as he did go here to shoot scenes. In the movie, his character never leaves the U.S.; in fact, he never leaves the CIA.)
While tightly edited, the Bourne Legacy, which now stars a new lead, did labor and spend a lot of screen time trying to fit itself into the whole Bourne scheme of things. It did so successfully—the franchise's puzzle pieces all fit soundly—but by the time Legacy has claimed its space in the film series, there is little time left to pursue a different direction and storyline. (Though it may as well have been a smart move: the ending begs for a sequel.)
The film wonderfully and faithfully captures the frenzy and organized chaos that is Manila, pulling off motorcycle chases in the middle of the city's traffic jam and wet markets. Although it was jarring to see well-known Filipino actors in their bit roles and hear security guards speak in a Filipino-American accent, I suppose these are nuances that only Filipino audiences would pick up.