First off, I have a few things to say:
I was wondering if anybody would be interested in diary entries of one of my favorite characters K'kruhk. I have great ideas about him having a pizza party.

And on to the tips...

Grievous on the run is a bonus mission that involves fighting droids and clones to get to the boss of the level: Obi-Wan.

The real trick to surviving the battle is to block constantly to deflect blaster bolts and follow with either your blaster or quick strikes.
When you get to Obi-wan the best method to defeat him is similar.
You block his primary attacks and attack with speed attacks. Repeat until you win.

May the force be with you all!