The World is Not Enough Walkthrough:
2: King's Ransom
In this mission, you are chasing down the assassin. Sadly, you don't get to do any of the water chase sequences - that's simply covered with the cut scene. You begin with the balloon popping, and you now chase the woman through the streets of the city. This wasn't in the movie, but heck, it's fun.
Grab the heavy armor to the right, and follow through buildings and streets, shooting as you go. You should find other armor in the various buildings, and another heavy armor down the second street. You'll go into a bar - be sure to only shoot the bad guys in here! Now you're back into the streets again, where you use a grappling hook on the balloon.
This is a pretty quick mission, and really it's just a matter of shooting well.
The World is Not Enough Walkthrough