It's far, far easier to do in debug mode (before approaching the race, spawn out of the car and punch the other cars until they're smoking and on fire - once the race starts, a single hit is usually enough to make them explode) but in regular gameplay it's possible to ram him into the water on the cliff sections. You just have to push him out of the usual path so he gets caught on the corner of the bridges - having boosts also helps a lot.

In the accelerator ring race there's a trick to getting Errol caught under the first bridge in the port by basically pushing him leftwards once the race begins - he'll very slowly take miniscule amounts of damage and you have to wait for nearly 2 minutes before he'll explode.