Maybe its just me but I think the description for this achievement is slightly misleading.
I think it ought to say:
Get 500 Takedowns (online *or* offline).
ie. You only need 500 offline takedowns OR 500 online takedowns, not both.
As Bleakdestiny said, you'll get this when you're playing through the offline missions to get your license, especially if you do a bunch of road rage and marked man missions.