Hire Car would be the quickest, although Seville is not a great place for cars.
Viamichelin.com shows the distance at 206km with a transit time of 2hrs 15mins.
The closest train station is at Algeciras some 20km away from Tarifa and you would have to take a bus to Algeciras.
There is a bus service operated by Transportes Generales Comes that operates from Tarifa to Sevilla four times daily.
You can find the timetable here: