On PS2, Jedi heroes can't be killed with conventional methods (blasters, grenades, mines etc). They can only be crushed by a vehicle or forced into a no-live zone (water on Theed, down a pit, etc).
On Bespin Platforms, it's very hard to kill a Jedi in the corridors, because you need to blow him through a window at just the right angle. A better method is to wait until he emerges onto a platform, then grenade/rocket him off.
On Bespin Cloud City, the only way I've found is to blow him off the bridge just outside the Carbon Freezing Chamber (NO! THAT CAN'T BE TRUE! THAT'S IMPOSSIBLE!... bye whiney Luke!)
On most other maps, you can run him over with a speeder or bigger vehicle and that does the trick.