This achievement is relatively simple to get. You start off on the bridge of the Resolute, a Republic warship, and you are trying to get to a Seperatist flagship, the Invisible Hand, which is the ship featured at the beginning of Episode III.
To start with, you need to have unlocked 10 gold bricks, which you will use to build some doors to access different areas of the ship. I'd suggest just playing through the missions, and when you've completed ten of them, then trying for this achievement. You must have completed one where you use a vehicle.
On the Ventress path (purple), the first mission with vehicles is Storm Over Ryloth, which is the fourth in line.
On the Grievous path (green), the first with vehicles is Shadow of Malevolence, which is the second mission in that line.
On the Dooku path (blue), the first is Jedi Crash, and the third mission in that strand with vehicles.
If you just play all the missions in one strand, you will unlock at least one vehicle, so from that perspective, it doesn't matter which one you choose, since you will need to complete at least one vehicle mission to get 10 gold bricks (unless you get True Jedi).
To get to the Invisible Hand, you have to go through a door that is immediately to the left of the console on the bridge, and requires 3 gold bricks. Go through this, and you will go down a lift to a reactor room. There is a short path to a central terminal that you can't interact with at the moment, and two other paths. One leads towards you, and the other away. Take this one to a door that has bars crossing it, and needs 10 gold bricks to access it. What occasionally seems to happen is you walk up to it and it doesn't open. Just go back a bit, and walk up to it again, and it will open.
You then need to walk down the straight path you will see, and go left towards a lift. Take it down, and you will find yourself in a hangar with a terminal close to you. Go up to it and press B, and the selection of vehicles available to you will appear. Pick which ever one you want, and it will come down from the ceiling and land behind the terminal. If they are flashing, it means you still have to buy it, so if you don't want to spend your studs, get one that you unlocked via a mission. You then press Y to get into the ship, and fly out of the hangar.
When you are in space, just keep flying right, and eventually you will come across another ship. There will be a big red arrow floating just outside the bay doors, and when you get close to it, press Y to land the ship. The achievement should unlock as soon as the ship touches down.
Credit to the video goes to XboxAchievables.