Anything is possible – especially if you have a unique talent, are exceptional in sports, have a hardship or disadvantage, or pick an off the grid major.
Since Berkeley does not publicly list the average GPA by major, the best way to figure it out is to look at UCLA’s Profile of Admitted Transfer Students and add approximately .1 to the GPA to determine the Berkeley equivalent. (This is the down and dirty strategy and maybe not too scientific.) The less sought after majors usually have lower admitted GPAs.
Try to find majors on the UCLA page in which you comfortably fit within the GPA parameters. As noted, there may also be extenuating circumstances that increase your odds. Also keep in mind, that GPA averages vary year to year, based on popularity cycles and size of department, among other factors.
If you are an under-represented applicant (minority, low income, or first generation), you can also improve your chances by enrolling in Berkeley’s TAP program, which is offered at select community colleges. According to the UC Berkeley website,TAP applicants have an admit rate close to 80%.
UPDATE, May 2016: Berkeley now lists GPA by major at: http://www.universityofcalifornia.edu/infocenter/transfers-major.