Hey there,
Here is the way to kill Jigsaw. (I'll also include a handy tip at the end, be sure to check it out).
Around the rooftop you're on during the final battle, there are little green things, (I forgot what they're called) they are kind of hidden behind stairwells and other objects.
Once you pick them up throw them by Jigsaw, move a safe distance away and shoot the bomb before Jigsaw moves too far away from it. Keep repeating the process to destroy him.
Remember- At the beginning of the batlle you have to shoot his jetpack until it breaks off and he falls to the ground. TIP- Ready for the tip?
Here it is: When you meet the wounded guard at the gate in the prison and he tells you to go up to the roof and destroy the generator, you can get a good tool to help destroy Jigsaw with.
Go up to the roof, destroy the generator then pick up the rocket launcher that's up there and keep it until the face off with Jigsaw. It saves you the trouble of having to collect some bombs.