The easiest way I found was to first unlock the Heavy APC (anti-tank weapon, extra armor).
If you're playing co-op this is a lot easier. I was the driver and just stayed in the APC, as such, I wasn't getting any damage, the APC was. And the APC is strong enough to destroy tanks! My two friends did the objectives and we drove to the extraction. Wait for the extraction and run to the dropship without getting hit.
Done and achievement unlocked.