To break 3-2 Chasm Crossing, you'll need to abuse Warp Beacon to skip past the death rail cutoff ramps. The process essentially consists of free-falling down the right side, occasionally stopping to warp your chariot by pressing
, then pressing
again. You have to cross the finish at 1:10:000 or quicker.
Note that my Warp Beacon is fully upgraded here. I didn't try it before upgrading, though I'm pretty sure you'll need it maxed out for this achievement.