you have to have good enough pokemon. but why would you defeat him and not catch him? do you not have any pokeballs? he is useful for battling aaron in the elite four if you put fly on him.
you get giritina in the distortion world. It really is quite simple
In the Distortion World after you got your seventh badge and defeat Cyrus for the second time, receiving a Master Ball
you have to beat Cyrus in the distortion world
well at the top of spear pillar but to you have to follow him into the distortion world where you can catch him.
It is found in the Distortion world- the entrance is at the spear pillar in Mt. Coronet
While playing through the story you will end up in the distortion world with Cynthia. in the distortion world you will have to battle Cyrus after beating him Cynthia will heal your Pokemon. then you will be able to find giritina, in the distortion world.
Giratina is not available in Leaf Green, he is catchable only in Platinum version.
In Pokemon Platinum, You Have To Go To Distortion World Which Is Available In The Storyline There, You Will Have a Wild Encounter With It.
Usually in the 'Distortion World'...but you have to climb Mt. Cornet...and battle Mars and Jupiter... But the good thing is you are stuck in the Distortion World with Cynthia, so you'll be okay... Oh, and don't worry if you haven't battled the Electric Gym Challenger...that is after the Distortion World...
You need to go east of the valor lakefront (south of veilstone and east of pastoria) after you battle giritina at the distortion world.
After you beat the Pokemon League, a path on Route 214 will open up called, Spring Path. You will need Rock Climb and possibly Surf. It will be the same cave that is in Peal and Diamond where you found/ find Giritina. But where Giritina was in Diamond and Pearl, will be the entrance to the Distortion World. Hope it helps. -CelestialIllusion
If you want to defeat GIRITINA just do it but use a quickball to do it that thing is ghost type so be carful