...that is a very strange computer. Less strange than what I first read, which was a gtx 680 and an A10, but still.
The AMD APUs are NOT competent processors. In order to get the onboard graphics (i.e. their selling point), the processing power gets gimped.
Battlefield is an extremely CPU-heavy game. Especially the multiplayer. It can tax a sandy bridge i5, or an FX 6100, quite hard - it doesn't surprise me at all that an A10 is flipping over and moaning at you.
You have a couple options. If your motherboard supports it, you could upgrade to an FX chip such as the FX 6350 or 8350.
The other option is buying a new motherboard and an intel I5 - if your budget supports it, I would recommend that route, as it's greater processing power, and should make absolutely sure you don't have a bottleneck there.