I have a Focus ZX3, zetech engine with 88K miles on it. I started noticing a really loud vibration coming from the dash/front end of the car, that reverberates as I am in reverse. It also vibrates in first and second gear a little bit, but doesn't vibrate in the 3-5th gears.

Dad thinks the clutch is going. Any other guesses?

You might have a bad motor/transmission mount. This will cause your driveline centerline to be thrown off, which will cause a vibration. Check for any cracks or tears in them. Good luck!