I use DuPont paint products, and 3-M finishing products. Go to a place
that sells automotive paint (call around to parts stores...) and get a
bottle of what is called 'glazing compound'. This is a very light
polishing compound, designed to get every last inch of shine out of a
paint job. You are less likely to burn through the clearcoat and paint
with this stuff.

Resist the urge to use power tools. Even I, and I've been at thsi for
some time, would not do this job with power tools. It will take a bit
of work, and be careful not to cut too deeply.

You won't make it 100%. I'm sure the clear coat is cracked down to the
base paint, and you don't want to take off the clear coat. Instead
what you want to do is simply cut off the sharp edges of the cracks so
they are less noticable.

I don't recommend the polishing compounds found in retail stores
(WalMart, etc.) as they are not the best quality. However, you could
try them if the glazing compound seems too expensive.

Good luck, work very slowly, and stop before you go too deep!