Each vehicle in the game has its own unlock criteria:

Monster - Complete Tropical 2 in under 1:08.00
Supercar - Complete Canyon 6 in under 1:26.00
Quad Bike - Complete Tropical Night 11 in under 1:03:00
Amphibian - Complete Artic 16 in under 1:01:00
Tank - Complete Artic 21 in under 1:10.00

Buggy - Complete Level 31 in under 1:28.00
Snowmobile - Complete Level 37 in under 1:00.00

Classic - Complete Level 46 in under 0:47.00

Alternatively you can unlock any vehicle with Gems.

Note: If the times in game no longer match the above please send us a support ticket to let us know