You will not get this achievement naturally playing through the game. You won't even come close.
The bad news is that the only way to get this achievement is farming.
The good news is that you can actually get it fairly quickly by farming, though it is still somewhat tedious and will likely take at least half an hour to get - though you will get several other achievements in the process.
The way to get this achievement is to go to the Scrollway level and farm the bonus round there. Boost over to the bonus round, go into it, get 4x coin multiplier, grab the big gem, restart the level. Rinse, repeat. You can get about 250k coins in 15 minutes or so of farming, so getting this achievement can take somewhere between 30-45 minutes, depending on how many coins you grabbed while beating the game.
You'll want to buy the necessary stuff to complete the Rainbow Rex, Shoe Shopping, Head Hunter, and Color Blast achievements along the way.