If you have a hero (Obi-Wan), then either hack at the AAA with your lightsaber or even do a lightsaber throw (L1) at them.
I have been doing the campaign using only stormtroopers (no heroes or villians) and only one life, so I have learned to be very careful with completing each level. On that map in particular, after achieving the first objective, a "chicken walker" appears near the start point. Jump in that thing and take the next two CPs (only hopping out to do the capture and/or fix them...you are an engineer, right?). When Grievous appears, I wail on him with the "chicken walker" again.
Keep your eyes peeled for a tank (IFX?) to appear either right before you whack the two AAA guns with your chicken walker or right after. The tank is a better pounder for the generator--get it.
The generator has hit areas that are not straight in front of it (if I recall correctly). So change (elevate?) your aim point until you not only get the words to show up correctly, but so that you get the "hit point" bar (that shows its health) as well. Then fire with both L1 and R1 until your guns overheat. Rinse and repeat.
Hope that helps.
* SithSpeeder *