My HD7950 can get ~60fps on BF4 ultra with x4 msaa, it might dip under but I overclocked my i5 and now it stays around 60.
for what you're wanting to do, you might need to get a 2500k/3570k and overclock it, or just not use MSAA, I didn't notice a huge difference without it to be honest.
also, the 14.11 driver and mantle wouldn't even let me play the game, look up on battlelog how many people are/were crashing with it...go back to 13.12 I believe, the last official stable AMD driver