The following vehicles can be unlocked by performing the actions below.

Hecthor - Win 1st in the Standard Cup
Xenum - Win 1st in the Expert-B Cup
Weimar - Win 1st in the Expert-A Cup
Velvet Works - Win 1st in the Master-B Cup
Sanctuary - Beat PRIMETIME in Timetrial mode
CALADRIUS in Timetrail mode - Finish 1st in Master-A Cup.
PRIMETIME in Timetrail mode - Beat CALADRIUS in Timetrail mode.