To reach an Overdrive multiplier of any amount you need to kill enemies within quick succession of each other. This is very likely to occur many times as you play through the game, but if for whatever reason you haven't managed this, you can unlock it during Mutant Bash TV. Play the normal challenge and then get yourself into the final round. The mutants here will spawn in big numbers and you can easily get 10 or more kills within quick enough succession to earn a multiplier of 10.