The mine cart ride is the last thing you do before entering the Church area and comes about 1/5 of the way through the game. It tasks you with jumping from track to track to collect coins and avoid dead ends.
EDIT: people have reported issues with being able to get this trophy after dashboarding. I could be wrong about passing checkpoints and then dashboarding to start over. Until I can test this out fully, plan on needing to get through the whole mine sequence your first try without missing coins or dying if you want to guarantee getting the achievement.
If you miss a coin or die, quickly dashboard (Xbox button, [cn_A], [cn_A]), force quit the game, then re-launch the game to try again. As long as you don't go through a checkpoint after making a mistake, you should be fine.