Yes, you will absolutely need a car. Get something tough and reliable to get you through traffic jams and extreme morning/afternoon heat. :)

Taxis are practically impossible to catch unless you are at one of the 2 major shopping malls (Vilaggio and City Center), where there is a designated area for pick-up/drop-off.

There is a bus service, but it does not run to all parts of the city. You'll find yourself stranded if you cannot cross a highway to get to a bus stop, for example, since there are no pedestrian bridges and very few safe crossings.