After the race of the 5th mission in the game, Lucas Bertone will talk to you, saying to drop by his shop some time because he got some goodies for you. Do just that before/after some later mission. Getting these cars isn't time-critical, like it used to be in the original game. In fact, you can also do all this in Free Roam and don't have to do it during the main campaign at all! Main Campaign is only important for how many of the 5 cars are unlocked, but I'm getting ahead of myself.

You will find his shop here:





Once inside, go and talk to him and he'll show you a board with 5 post cards on it:



Depending on how far you are in the story, you can pick up some/all of them. These cards give you a rough location and a hint as to where to find the cars. But don't fret, for I have done the work of finding them for you!

If you couldn't pick up all of them, try again after a couple of missions. After "A trip to the country" I had unlocked 2/5 and after "Bon Apetit" 4/5. The last car gets unlocked either after "Lucky Bastard" or "Creme de la Creme" - I didn't check which one, but probably the latter.

P.S: There are some more cars to unlock via the small Bonus Missions in Free Ride. However, these are NOT needed for the Achievement "Car Thief Number One".

Unless you associate the tip of "electric eel" with the dam up north, finding this car could take a lot of time as you have to basically search the whole countryside for the motel in the post card. But once you find the motel (to the far north, directly before the dam) it is quite easy to get it.

The rough location of the car is a little easier to find this time, but getting to it is another question. "The neighbors got a new toy" should give you a hint tho, once you find the mansion from the post card. Anyway, here is where the actual car is:





Beware tho - the owner is waiting for you inside that garage with a knife and won't let you steal his car without a fight. Also, a policeman is patroling the vicinity so be careful!

You could be searching quite a long time for this one if you don't realize what the post card is telling you - but it's worth it. If you wished you could keep the race car from "Fair Play", then this is the car for you.

Look for the construction crane in the post card and once you found the location of the skyscraper being built (directly by the bridge), finding the car is a piece of cake.

My favourite car from the previous game! Unfortunately it isn't as kick-ass as in the previous one, but oh well. Also, there are reports that this car might not spawn for some people. It spawned for me, but if it didn't for you, you might want to send a bug report to the devs!

Anyway, getting to this one is a bit more difficult than the last 3. First you have to find the entrance to the Freight department of the Central Main Station.





Climb up the crates to the right in the above picture and above the wall to find yourself in a "maze". As oriented in the above picture, you want to continue towards the top right. It isn't really difficult whatsoever as there are basically no dead ends - you have to climb over some crates to get there though, but I'm sure you'll manage. Lastly, kick in a door and the car is yours.

This car is at the same time the easiest to find but the hardest to get. As the postcard suggests, it is wise to bring a gun for this one.



Armed with your weapon of choice, make your way towards downtown. Luckily, this time you get told the exact location of the car: Waterfront, so just drive to that point on the map.





Once there you have to kick in that door and for the eagle-eyed, you can already spot your prize through the slit in the middle gate.

Once inside you will be greeted by a couple of boxes. Shoot them. Or punch them. But shooting is more fun.



You'll have to do this a couple more times and there you are, congratulations on your new Trautenberg!



At this point you'll already have the car unlocked for your garage and should've gotten your achievement (provided you took care of the other 4 first). But to really finish, you now need the wits part of "piece and wits". There are three levers that want to be pulled in the correct order at threat of being knocked out if you fail to do so. To find the correct combination, take a look again at the post card and it should reveal you the correct order:
Middle, then left, then right.
Now the gate should open and the final hidden car is yours!



TL;DR: Light Combination is Middle-Left-Right. Take gun and do the shoot-shoot on the crate-crates.