For those who still got trouble with this, here is a tip. I did evereything described with Frank's car and the achivement did't pop. After that i went to the LS Customs that you can buy and i bought. Did everthing again with a random sedan car and then i got the achievement.
Make sure you buy the tires stuff (smoke, bullet proof, etc)
The Neon lights
Turn off the auto save berfore doing this so you don't lose your money.