First off, you're going to be killing Mel's buddies before you take on the big guy, himself. The first wave is just the smaller guys. The second wave comes with Mel. If you're low on shields at the end of the first wave, leave the last guy until they've powered back up, then finish him off and face the second wave.
To kill Mel, himself, you'll want a car which has a machine gun mount. Lock your targeting in on Mel (by pressing the space bar), then just run and gun. Alternatively, you can run around the stage and use a corrosive weapon to destroy his vehicle, however this is very risky.
If you prefer to use a car with a cannon mount, the easiest way to take Mel out is by driving in reverse. Driving backwards, keep circling the center stage. As Mel is driving around the stage in pursuit, lob a cannon shot at him and immediately make a sharp turn around the stage. Mel's answering shot should miss you if you do this correctly. This maneuver isn't too difficult with a mouse and keyboard, but X-box players may have trouble.
If you are still having trouble, you could try the cheap way out. Don't completely enter the arena. Stand on the raised platform and just start shooting. This method will not get you killed, but it takes quite a while as well.