To access Ground Battle for the Republic, you must have access to particular control console. To get there from the main hub, go down the elevator on your left and head to the far right corner with the metal grating. Once through, take the elevator to the right, which requires gold bricks (I believe 40) and go through there.
After you get down there, you will need to buy a heavy vehicle to blow through the locked grating in the middle of the room. (I suggest the AT-AP) That is the ground assault console you see through it. Note that all planets in the system must be converted to Republic (Blue) at the same time in order for the achievement to unlock.
While working for the 100% achievement, once every system has been converted to Separatist once, you will unlock Chancellor Palpatine as a playable character. Note that if a system begins under Republic control it must be converted to Separatist and then back to Republic in order to unlock the character.
Ground Assault Tactics:
Always pick a heavy vehicle to start with as they can take care of all basic and silver bases quickly and efficiently leaving only gold structures to deal with later.
Republic: AT-AP Walker or Pirate Speeder Tank
Separatist: Pirate Speeder Tank, AAT or Super Tank.
Destroy Statues: Focus first on what protects the statues followed by destroying the statues themselves. Do not waste time destroying enemy bases.
Build Escape Pod: Eliminate all nearby bases, pausing to build the newest available building in the area once the base has been wiped. Build your Escape Pod on the same base you built your shield for added protection. Destroy only what you need to.
Destroy Enemy Command Center: Focus on what protects that Command Center and eliminate all protection first. The give everything you've got to crushing the Command Center.
Destroy All Enemy Buildings: The best advice for this one is to use the small Speeder Bikes or something along those lines. They may be slower than a heavy vehicle, but they can destroy any building on the map without having to worry about chasing down a different vehicle.